Publikationer 2019

A Bound on Thermal Relativistic Correlators at Large Spacelike Momenta

Authors: Souvik Banerjee, Kyriakos Papadodimas, Suvrat Raju, Prashant Samantray, Pushkal Shrivastava

Preprint number: UUITP-7/19

We consider thermal Wightman correlators in a relativistic quantum field theory in the limit where the spatial momenta of the insertions become large while their frequencies stay fixed. We show that, in this limit, the size of this correlator is bounded by exp(-βR) where R is the radius of the smallest sphere that contains the polygon formed by the momenta. We argue that, generically, perturbative quantum field theories can saturate this bound through suitably high-order loop diagrams. We also consider holographic theories in d-spacetime dimensions where we show that the leading two-point function of generalized free-fields in such theories saturates the bound in d = 2 and is below the bound for d > 2. We briefly discuss interactions in holographic theories and conclude with a discussion of several open problems.

Constructing stable de Sitter in M-theory from higher curvature corrections

Authors: Johan Blåbäck, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri

Preprint number: UUITP-6/19

We consider dimensional reductions of M-theory on T⁷/ℤ₂³ with the inclusion of arbitrary metric flux and spacetime filling KK monopoles. With these ingredients at hand, we are able to construct a novel family of non-supersymmetric yet tachyon free Minkowski extrema. These solutions are supported by pure geometry with no extra need for gauge fluxes and possess a fully stable perturbative mass spectrum, up to a single flat direction. Such a direction corresponds to the overall internal volume, with respect to which the scalar potential exhibts a no-scale behavior. We then provide a mechanism that lifts the flat direction to give it a positive squared mass while turning Mkw₄ into dS₄ The construction makes use of the combined effect of G₇ flux and higher curvature corrections. Our solution is scale separated and the qunatum corrections are small. Finally we speculate on novel possibilities when it comes to scale hierarchies within a given construction of this type, and possible issues with the choice of quantum vacuum.

The fate of the Konishi multiplet in the β-deformed Quantum Spectral Curve

Authors: Christian Marboe, Erik Widen

Preprint number: UUITP-5/19

We investigate the solution space of the β-deformed Quantum Spectral Curve by studying a sample of solutions corresponding to single-trace operators that in the undeformed theory belong to the Konishi multiplet. We discuss how to set the precise boundary conditions for the leading Q-system for a given state, how to solve it, and how to build perturbative corrections to the Pμ-system. We confirm and add several loop orders to known results in the literature.

Boundary gauge and gravitational anomalies from Ward identities

Author:Vladimir Prochazka

Preprint number: UUITP-4/19

Abstract: We consider the two-point functions of conserved bulk currents and energy-momentum tensor in a boundary CFT defined on $\mathbb{R}_-^{1,2}$. Starting from the consistent forms of boundary gauge and gravitational anomalies we derive their respective contributions to the correlation functions in the form of anomalous Ward identities. Using the recently developed momentum space formalism we find an anomalous solution to each of these identities depending on a single undetermined form-factor. We study the solution in two different kinematic limits corresponding to small and large momentum $p_n$, perpendicular to the boundary. We find that the anomalous term interpolates between a non-local form resembling the standard anomaly-induced term in a two-dimensional CFT at small $p_n$ and Chern-Simons contact terms at large $p_n$. Using this we derive some consistency conditions regarding the dependence of these anomalies on the boundary conditions and discuss possible cancellation mechanisms. These ideas are then demonstrated on the explicit example of free, massless three-dimensional fermion. In particular we manage to obtain the respective anomalies via a diagrammatic momentum space computation and expose the well-known relation between bulk parity anomaly and boundary gauge anomalies.

Cardy-like asymptotics of the 4d N=4 index and AdS_5 blackholes

Author: Arash Arabi Ardehali

Preprint number: UUITP-3/19

Choi, Kim, Kim, and Nahmgoong have recently pioneered analyzing a Cardy-like limit of the superconformal index of the 4d N=4 theory with complexified fugacities which encodes the entropy of the dual supersymmetric AdS_5 blackholes. Here we study the Cardy-like asymptotics of the index within the rigorous framework of elliptic hypergeometric integrals, thereby filling a gap in their derivation of the blackhole entropy function, finding a new blackhole saddle-point, and demonstrating novel bifurcation phenomena in the asymptotics of the index as a function of fugacity phases. We also comment on the relevance of the supersymmetric Casimir energy to the blackhole entropy function in the present context.

Branes, partition functions and quadratic monopole superpotentials

Authors: Antonio Amariti, Luca Cassia, Ivan Garozzo, Noppadol Mekareeya

Preprint number: UUITP-2/19

We obtain the brane setup describing 3d N=2 dualities for USp(2Nc) and U(Nc) SQCD with monopole superpotentials. This classification follows from a complete analysis of affine and twisted affine compactifications from 4d. The analysis leads to a new duality for the unitary case that has been previously overlooked in the literature. We check this by matching of the three sphere partition function of the two sides of this new duality and find a perfect agreement. Furthermore we use the partition function to predict new 3d N=2 dualities for SQCD with monopole superpotentials and tensorial matter.

N = 2* Phase Transitions and Holography

Authors: Jorge G. Russo, Erik Widen, Konstantin Zarembo

Preprint number: UUITP-1/19

We clarify the relationship between probe analysis of the supergravity dual and the large-N solution of the localization matrix model for the planar N = 2* super-Yang-Mills theory. A formalism inspired by supergravity allows us to systematically solve the matrix model at strong coupling. Quite surprisingly, we find that quantum phase transitions, known to occur in the N = 2* theory, start to be visible at the third order of the strong-coupling expansion and thus constitute a perturbative phenomenon on the string worldsheet.

A Refined N=2 Chiral Multiplet on Twisted AdS_2 x S^1

Authors: Antonio Pittelli

Preprint number: UUITP-63/18

Non-Abelian gauged supergravities as double copies

Authors: Marco Chiodaroli, Murat Gunaydin, Henrik Johansson and Radu Roiban

Preprint number: UUITP-62/18

The full spectrum of AdS5/CFT4 II: Weak coupling expansion via the quantum spectral curve

Authors: Christian Marboe, Dmytro Volin

Preprint number: UUITP-61/18

We continue the effort to optimise and generalise the solution of the spectral problem of AdS5/CFT4 in the planar limit via integrability. We present a simple strategy to solve the quantum spectral curve perturbatively for general states by focusing on the Pμ-system. A Mathematica notebook with an implementation of this algorithm is provided, as well as an extensive database  with a user-friendly interface containing more than 8.000 solutions of the QSC. When investigating the solution space, we observe a curious phenomenon: existence of solutions for which the Q-system degenerates in the limit g->0. These degeneracies are lifted at higher orders in perturbation theory. The degenerating solutions have auxiliary Bethe roots merging with branch points at weak coupling.

Evolution for Khovanov polynomials for figure-eight-like family of knots

Authors: Petr Dunin-Barkowski, Aleksandr Popolitov, Svetlana Popolitova

Preprint number: UUITP-60/18

 We look at how evolution method deforms, when one considers Khovanov polynomials instead of Jones polynomials. We do this for the figure-eight-like knots -- a two-parametric family of knots which "grows" from the figure-eight knot and contains both two-strand torus knots and twist knots. We prove that parameter space splits into four chambers, each with its own evolution, and two isolated points. Remarkably, the evolution in the Khovanov case features an extra eigenvalue, which drops out in the Jones (t -> -1) limit.

Twisting with a Flip (the Art of Pestunization)

Authors: Guido Festuccia, Jian Qiu, Jacob Winding, Maxim Zabzine

Preprint number: UUITP-59/18

 We construct  N=2 supersymmetric Yang-Mills theory on 4D manifold with Killing vector field with the isolated fixed points. It turns out that for every fixed point one can allocate either instanton or anti-instanton contributions in the partition function and this is compatible with the supersymmetry. The equivariant Donaldson-Witten theory is a special case of our construction. We present the unified treatment of the Pestun's calculation on S^4 and the equivariant Donaldson-Witten theory by generalizing the notion of self-duality on the manifolds with a vector field. We conjecture the full partition function for N=2 theory on any 4D simply connected manifold with a Killing vector.   

String amplitudes from QFT amplitudes and vice versa

Author: Song He, Fei Teng and Yong Zhang

Preprint number: UUITP-58/18

We present an integration-by-part reduction of any massless tree-level string correlator to an equivalence class of ``logarithmic functions'', which can be used to define a field-theory amplitude via a Cachazo-He-Yuan (CHY) formula. The string amplitude is then shown to be the double copy of the field theory one and a special disk/sphere integral. The construction is generic as it applies to any correlator that is a rational function of correct SL$(2)$ weight. By applying the reduction to open bosonic/heterotic strings, we get a closed-form CHY integrand for the $DF^2+\text{YM}+\phi^3$ theory.

One-loop Amplitudes for N = 2 Homogeneous Supergravities

Authors: Maor Ben-Shahar and Marco Chiodaroli

Preprint number: UUITP-57/18

Quantum Corrections to Central Charges and Supersymmetric Casimir Energy in AdS3/CFT2

Authors: Arash Arabi Ardehali, Finn Larsen, James T. Liu, Phillip Szepietowski

Preprint number: UUITP-56/18

We study the Casimir energy of bulk fields in AdS3 and its relation to subleading terms in the central charge of the dual CFT2. Computing both sides of the standard CFT2 relation E=−c/12 independently we show that this relation is not necessarily satisfied at the level of individual bulk supergravity states, but in theories with sufficient supersymmetry it is restored at the level of bulk supermultiplets. Assuming at least (0,2) supersymmetry, we improve the situation by relating quantum corrections to the central charge and the supersymmetric Casimir energy which in turn is related to an index. These relations adapt recent progress on the AdS5/CFT4 correspondence to AdS3/CFT2 holography. We test our formula successfully in several examples, including the (0,4) MSW theory describing classes of 4D black holes and the large (4,4) theory that is interesting for higher spin holography. We also make predictions for the subleading central charges in several recently proposed (2,2) dualities where the CFT2 is not yet well-understood.

AdS2 solutions and their massive IIA origin

Authors: Giuseppe Dibitetto and Nicolò Petri

Preprint number: UUITP-55/18

We consider warped AdS2 x M4 backgrounds within F(4) gauged supergravity in six dimensions. In particular, we are able to find supersymmetric solutions of the aforementioned type characterized by AdS6 asymptotics and an M4 given by a three-sphere warped over a segment. Subsequently, we provide the 10D uplift of the solutions to massive type IIA supergravity, where the geometry is AdS2 x S3 x S3 warped over a strip. Finally we construct the brane intersection underlying one of these supergravity backgrounds. The explicit setup involves D0 - F1 - D4 bound state intersecting a D4 - D8 system.

Two-loop N = 2 SQCD amplitudes with external matter from iterated cut

Authors: Gregor Kälin, Gustav Mogull, Alexander Ochirov

Preprint number: UUITP-54/18

We develop an iterative method for constructing four-dimensional generalized unitarity cuts in N = 2 supersymmetric Yang-Mills (SYM) theory coupled to fundamental matter hypermultiplets (N = 2 SQCD). For iterated two-particle cuts, specifically those involving only four-point amplitudes, this implies simple diagrammatic rules for assembling the cuts to any loop order, analogous to the rung rule in N = 4 SYM. By identifying physical poles, the construction simplifies the task of extracting complete integrands. In combination with the duality between color and kinematics we construct all four-point massless MHV-sector scattering amplitudes up to two loops in N = 2 SQCD, including those with matter on external legs. Our results reveal chiral infrared-finite integrands closely related to those found using loop-level BCFW recursion. The integrands are valid in D ≤ 6 dimensions with external states in a four-dimensional subspace; the upper bound is dictated by our use of six-dimensional chiral N = (1, 0) SYM as a means of dimensionally regulating loop integrals.

Physics and geometry of knots-quivers correspondence

Authors: Tobias Ekholm, Piotr Kucharski, Pietro Longhi

Preprint number: UUITP-53/18

Gauge theories on spheres with 16 supercharges and non-constant couplings

Authors: Joseph A. Minahan and Usman Naseer

Preprint number: UUITP-52/18

T-Duality in (2,1) Superspace

Preprint number: UUITP-51/18

Authors: M. Abou-Zeid, C. M. Hull, U. Lindström and M. Roček

Abstract: We find the T-duality transformation rules for 2-dimensional (2,1) supersymmet- ric sigma-models in (2,1) superspace. Our results clarify certain aspects of the (2,1) sigma model geometry relevant to the discussion of T-duality. The complexified duality transformations we find are equivalent to the usual Buscher duality trans- formations (including an important refinement) together with diffeomorphisms. We use the gauging of sigma-models in (2,1) superspace, which we review and develop, finding a manifestly real and geometric expression for the gauged action. We discuss the obstructions to gauging (2,1) sigma-models, and find that the obstructions to (2,1) T-duality are considerably weaker.

A new light on the darkest corner of the landscape

Preprint number: UUITP-50/18

Authors: Johan Blåbäck, Ulf Danielsson and Giuseppe Dibitetto

Abstract: Motivated by the recently proposed bounds on the slow-roll parameters for
scalar potentials arising from string/M-theory compactifications, a.k.a. the
Refined de Sitter Swampland conjecture, we explore the sharpness of such
constraints within 4D supergravities coming from compactifications of massive
type IIA string theory on T 6 /(Z 2 × Z 2 ). With the aid of a numerical technique,
known as differential evolution, we are able to find a de Sitter extremum which
is fully metastable up to one single flat direction. This solution is supported by
spacetime filling sources such as O6 planes and KK monopoles. Our example
violates the bound imposed by this conjecture.

Separated variables and wave functions for rational gl(N) spin chains in the companion twist frame

Authors: Paul Ryan and Dmytro Volin

Preprint number: UUITP-49/18

We propose a basis for rational gl(N) spin chains in an arbitrary rectangular representation (S^A) that factorises the Bethe vectors into products of Slater determinants in Baxter Q-functions. This basis is constructed by repeated action of fused transfer matrices on a suitable reference state. We prove that it diagonalises the so-called B-operator, hence the operatorial roots of the latter are the separated variables. The spectrum of the separated variables is also explicitly computed and it turns out to be labelled by Gelfand-Tsetlin patterns. Our approach utilises a special choice of the spin chain twist which substantially simplifies derivations.

Dyson equations for correlators of Wilson loops

Authors: Diego Correa, Pablo Pisani, Alan Rios Fukelman and Konstantin Zarembo

Preprint Number: UUITP-48/18

By considering a Gaussian truncation of N=4 super Yang-Mills, we derive a set of Dyson equations that account for the ladder diagram contribution to connected correlators of circular Wilson loops. We consider different numbers of loops, with different relative orientations. We show that the Dyson equations admit a spectral representation in terms of eigenfunctions of a Schrödinger problem, whose classical limit describes the strong coupling limit of the ladder resummation. We also verify that in supersymmetric cases the exact solution to the Dyson equations reproduces known matrix model results.

Boundary and Defect CFT: Open Problems and Applications

Authors: Natan Andrei, Agnese Bissi, Matthew Buican, John Cardy, Patrick Dorey, Nadav Drukker, Johanna Erdmenger, Daniel Friedan, Dmitri Fursaev, Anatoly Konechny, Charlotte Kristjansen, Isao Makabe, Yu Nakayama, Andy O'Bannon, Robert Parini, Brandon Robinson, Shinsei Ryu, Cornelius Schmidt-Colinet, Volker Schomerus, Christoph Schweigert, Gerard Watts

Preprint number: UUITP-47/18

Proceedings of the workshop "Boundary and Defect Conformal Field Theory: Open Problems and Applications," Chicheley Hall, Buckinghamshire, UK, 7-8 Sept. 2017.

The Generalised Complex Geometry of SKT Spaces and (p,q) Supersymmetric Sigma Models

Authors: Chris Hull and Ulf Lindström

Preprint number: UUITP-46/18

We provide a   generalised complex geometry formulation of the target space geometry of the (p,q) supersymmetric sigma model. This includes generalized Kähler geometry for (2,2), generalized hyperkähler geometry for (4,2), strong Kähler with torsion geometry for (2,1) and strong hyperkähler with torsion geometry for (4,1). Our formulation involves a chiral version of generalised complex structure.

Solving q-Virasoro constraints

Authors: Rebecca Lodin, Aleksandr Popolitov, Shamil Shakirov, Maxim Zabzine

Preprint number: UUITP-44/18

We show how q-Virasoro constraints can be derived for a large class of (q,t)-deformed eigenvalue matrix models by an elementary trick of inserting certain q-difference operators under the integral, in complete analogy with full-derivative insertions for β-ensembles. From free field point of view the models considered have zero momentum of the highest weight, which leads to an extra constraint T_{−1}Z = 0. We then show how to solve these q-Virasoro constraints recursively and comment on the possible applications for gauge theories, for instance calculation of (supersymmetric) Wilson loop averages in gauge theories on D^2 × S^1 and S^3.

Counting String Theory Standard Models

Authors: Andrei Constantin, Yang-Hui He, Andre Lukas

Preprint number: UUITP-43/18

We derive an approximate analytic relation between the number of consistent heterotic Calabi-Yau compactifications of string theory with the exact charged matter content of the standard model of particle physics and the topological data of the internal manifold: the former scaling exponentially with the number of Kähler parameters. This is done by an estimate of the number of solutions to a set of Diophantine equations representing constraints satisfied by any consistent heterotic string vacuum with three chiral massless families, and has been computationally checked to hold for complete intersection Calabi-Yau threefolds (CICYs) with up to seven Kähler parameters. When extrapolated to the entire CICY list, the relation gives ∼10^23 string theory standard models; for the class of Calabi-Yau hypersurfaces in toric varieties, it gives ∼10^723 standard models.

Genus-One String Amplitudes from Conformal Field Theory

Authors: Luis F. Alday, Agnese Bissi, Eric Perlmutter

Preprint number: UUITP-42/18

We explore and exploit the relation between non-planar correlators in N = 4 super-Yang-Mills, and higher-genus closed string amplitudes in type IIB string theory. By conformal field theory techniques we construct the genus-one, four-point string amplitude in AdS5 × S5 in the low-energy expansion, dual to an N = 4 super-Yang-Mills correlator in the ’t Hooft limit at order 1/c^2 in a strong coupling expansion. In the flat space limit, this maps onto the genus-one, four-point scattering amplitude for type II closed strings in ten dimensions. Using this approach we reproduce several results obtained via string perturbation theory. We also demonstrate a novel mechanism to fix subleading terms in the flat space limit of AdS amplitudes by using string/M-theory.

6D attractors and black hole microstates

Authors: Seyed Morteza Hosseini, Kiril Hristov, Achilleas Passias, and Alberto Zaffaroni
Preprint number: UUITP-41/18

Berends–Giele currents in Bern–Carrasco-Johansson gauge for F^3- and F^4-deformed Yang–Mills amplitudes

Authors: Lucia M. Garozzo, Leonel Queimada, Oliver Schlotterer

Preprint number: UUITP-40/18

We construct new representations of tree-level amplitudes in D-dimensional gauge theories with deformations via higher-mass-dimension operators \alpha' F^3 and \alpha'^2 F^4. Based on Berends—Giele recursions, the tensor structure of these amplitudes up to the order of \alpha’^2 is compactly organized via off-shell currents. On the one hand, we present manifestly cyclic representations, where the complexity of the currents is systematically reduced. On the other hand, the duality between color and kinematics due to Bern, Carrasco and Johansson is manifested by means of non-linear gauge transformations of the currents. We exploit the resulting notion of Bern--Carrasco--Johansson gauge to provide explicit and manifestly local double-copy representations for gravitational amplitudes involving \alpha' R^2 and \alpha'^2 R^3 operators.

The quantum swampland

Authors: Ulf H. Danielsson

Preprint number: UUITP-39/18

(1,0) gauge theories on the six-sphere

Authors: Usman Naseer

Preprint number: UUITP-38/18

We construct gauge theories with a vector-multiplet and hypermultiplets of (1,0) supersymmetry on the six-sphere. The gauge coupling on the sphere depends on the polar angle. This has a natural explanation in terms of the tensor branch of (1,0) theories on the six-sphere. For the vector-multiplet we give an off-shell formulation for all supersymmetries. For hypermultiplets we give an off-shell formulation for one supersymmetry. We show that the path integral for the vector- multiplet localizes to solutions of the Hermitian-Yang-Mills equation, which is a generalization of the (anti-)self duality condition to higher dimensions. For the hypermultiplet, the path integral localizes to configurations where the field strengths of two complex scalars are related by an almost complex structure.

3d Mirror Symmetry from S-duality

Authors: Fabrizio Nieri, Yiwen Pan, Maxim Zabzine

Preprint number: UUITP-37/18

Formulae for Line Bundle Cohomology on Calabi-Yau Threefolds

Authors: Andrei Constantin and Andre Lukas

Preprint number: UUITP-36/18

Abstract: We present closed form expressions for the ranks of all cohomology groups of holomorphic line bundles on several Calabi-Yau threefolds realised as complete intersections in products of projective spaces. The formulae have been obtained by systematising and extrapolating concrete calculations and they have been checked computationally. Although the intermediate calculations often involve laborious computations of ranks of Leray maps in the Koszul spectral sequence, the final results for cohomology follow a simple pattern. The space of line bundles can be divided into several different regions, and in each such region the ranks of all cohomology groups can be expressed as polynomials in the line bundle integers of degree at most three. The number of regions increases and case distinctions become more complicated for manifolds with a larger Picard number. We also find explicit cohomology formulae for several non-simply connected Calabi-Yau threefolds realised as quotients by freely acting discrete symmetries. More cases may be systematically handled by machine learning algorithms.

Analytic Bootstrap for Boundary CFT

Authors: Agnese Bissi, Tobias Hansen, Alexander Söderberg

Preprint number: UUITP-35/18

Abstract: We propose a method to analytically solve the bootstrap equation for two point functions in boundary CFT. We consider the analytic structure of the correlator in Lorentzian signature and in particular the discontinuity of bulk and boundary conformal blocks to extract CFT data. As an application, the correlator ⟨ϕϕ⟩ in ϕ^4 theory at the Wilson-Fisher fixed point is computed to order ϵ^2 in the ϵ expansion.

All five-loop planar four-point functions of half-BPS operators in N=4 SYM

Authors : Dmitry Chicherin, Alessandro Georgoudis, Vasco Goncalves and Raul Pereira

Preprint number: UUITP-34/18

We obtain all planar four-point correlators of half-BPS operators in N=4 SYM up to five loops. The ansatz for the integrand is fixed partially by imposing light-cone OPE relations between different correlators. We then fix the integrated correlators by comparing their asymptotic expansions with simple data obtained from integrability. We extract OPE coefficients and find a prediction for the triple wrapping correction of the hexagon form factors, which contributes already at the five-loop order.

Bootstrapping the S5 partition function

Authors: Fabrizio Nieri, Yiwen Pan, Maxim Zabzine

Preprint number: UUITP-33/18

Abstract: We consider U(N) SQCD on S5 and propose a Higgs branch-like expression for its partition function. We support the result by arguing that the knowledge of certain BPS codimension 2 and 4 defects arising from Higgsing is enough to reconstruct the bulk partition function, and that the defect partition functions satisfy a set of non-perturbative Schwinger-Dyson equations. We show that the result is consistent with, and naturally come from, the BPS/CFT perspective. In this language, the defect partition functions are identified with free boson correlators of the q-Virasoro modular triple, and the constraint equations with Ward identities satisfied by the corresponding Dotsenko-Fateev q-conformal blocks, providing a natural basis to expand the S5 partition function.

Surface defects in the D4-D8 brane system

Authors: Giuseppe Dibitetto and Nicolò Petri

Preprint number: UUITP-32/18

Abstract: A new class of exact supersymmetric solutions is derived within minimal d = 6 F(4) gauged supergravity. These flows are all characterized by a non-trivial radial profile for the 2-form gauge potential included into the supergravity multiplet. In particular three solutions within this class are featured by an AdS3 foliation of the 6d background and by an AdS6 asymptotic geometry. Secondly, considering the simplest example of these, we give its massive IIA uplift describing a warped solution of the type AdS3 × S2 × S3 fibered over two intervals I _r × I_ξ . We interpret this background as the near-horizon of a D4-D8 system on which a bound state D2-NS5-D6 ends producing a surface defect. Finally we discuss its holographic dual interpretation in terms of a N = (0, 4) SCFT2 defect theory within the N = 2 SCFT5 dual to the AdS6 × S4 massive IIA warped vacuum.

On the a-theorem in the Conformal Window

Authors: Vladimir Prochazka, Roman Zwicky

Preprint number: UUITP-30/18

Abstract:

We show that for four dimensional gauge theories in the conformal window, the Euler anomaly, known as the $a$-function, can be computed from a $2$-point function of the trace of the energy momentum tensor making them more amenable to lattice simulations. Concretely, we derive an expression for the $a$-function as an integral over the renormalisation scale of quantities related to $2$- and $3$-point functions of the trace of the energy momentum tensor.The crucial ingredients are that the square of the field strength tensor is an exactly marginal operator at the Gaussian fixed point and that the relevant $3$-point correlation function is finite when resummed to all orders. This allows us to define a scheme for which the $3$-point contribution vanishes, thereby explicitly establishing the strong version of the $a$-theorem for this class of theories.

AdS3 solutions with exceptional supersymmetry

Authors: Giuseppe Dibitetto, Gabriele Lo Monaco, Achilleas Passias, Nicolò Petri, Alessandro Tomasiello

Preprint number:  UUITP-29/18

Abstract:  Among the possible superalgebras that contain the AdS3 isometries, two interesting possibilities are the exceptional F(4) and G(3). Their R-symmetry is respectively SO(7) and G2, and the amount of supersymmetry N= 8 and N= 7. We find that there exist two (locally) unique solutions in type IIA supergravity that realize these superalgebras, and we provide their analytic expressions. In both cases, the internal space is obtained by a round six-sphere fibred over an interval, with an O8-plane at one end. The R-symmetry is the symmetry group of the sphere; in the G(3) case, it is broken to G2 by fluxes. We also find several numerical N= 1 solutions with G2 flavor symmetry, with various localized sources, including O2-planes and O8-planes.

Some remarks on (super)-conformal Killing-Yano tensors

Authors: P.S. Howe, and U. Lindström

Holographic duals of five-dimensional SCFTs on a Riemann surface

Authors: Ibrahima Bah, Achilleas Passias and Peter Weck

Preprint number: UUITP-28/18

We study the twisted compactifications of five-dimensional Seiberg SCFTs, with SU_M(2) x E_{N_f+1} flavor symmetry, on a generic Riemann surface that preserves four supercharges.  The five-dimensional SCFTs are obtained from the decoupling limit of N D4-branes probing a geometry of N_f<8 D8-branes and an O8-plane.  In addition to the R-symmetry, we can also twist the flavor symmetry by turning on background flux on the Riemann surface.  In particular, in the string theory construction of the five-dimensional SCFTs, the background flux for the SU_M(2) has a geometric origin, similar to the topological twist of the R-symmetry.  We argue that the resulting low-energy three-dimensional theories describe the dynamics on the world-volume of the N D4-branes wrapped on the Riemann surface in the O8/D8 background.  The Riemann surface can be described as a curve in a Calabi-Yau three-fold that is a sum of two line bundles over it.  This allows for an explicit construction of AdS_4 solutions in massive IIA supergravity dual to the world-volume theories, thereby providing strong evidence that the three-dimensional SCFTs exist in the low-energy limit of the compactification of the five-dimensional SCFTs.  We compute observables such as the free energy and the scaling dimensions of operators dual to D2-brane probes; these have non-trivial dependence on the twist parameter for the U(1) in SU_M(2).  The free energy exhibits the N^{5/2} scaling that is emblematic of five-dimensional SCFTs.

Emergent de Sitter cosmology from decaying AdS

Authors: Souvik Banerjee, Ulf Danielsson, Giuseppe Dibitetto, Suvendu Giri and Marjorie Schillo

Preprint number: UUITP-27/18

Recent developments in string compactifications demonstrate obstructions to the simplest constructions of low energy cosmologies with positive vacuum energy. The existence of obstacles to creating scale-separated de Sitter solutions indicates a UV/IR puzzle for embedding cosmological vacua in a unitary theory of quantum gravity. Motivated by this puzzle, we propose an embedding of positive energy Friedmann-Lemaître-Robertson-Walker cosmology within string theory. Our proposal involves confining 4D gravity on a brane which mediates the decay from a non-supersymmetric false AdS5 vacuum to a true vacuum. In this way, it is natural for a 4D observer to experience an effective positive cosmological constant coupled to matter and radiation, avoiding the need for scale separation or a fundamental de Sitter vacuum.

AdS2 x S7 solutions from D0 - F1 - D8 intersections

Authors: Giuseppe Dibitetto and Achilleas Passias
Preprint number: UUITP-26/18

We study an exhaustive analytic class of massive type IIA backgrounds preserving sixteen real supercharges and enjoying SL(2, R) x SO(8) bosonic symmetry. The corresponding geometry is described by AdS2 × S7 warped over a line, which turns out to emerge from taking the near-horizon limit of D0 - F1 - D8 intersections. By studying the singularity structure of these solutions we find the possible presence of localized O8/D8 sources, as well as of fundamental strings smeared over the S7 . Finally we discuss the relation between the aforementioned solutions and the known AdS7 x S2 class through double analytic continuation.

General Relativity from Scattering Amplitudes

Authors: N.E.J. Bjerrum-Bohr, Poul H. Damgaard, Guido Festuccia, Ludovic Planté and Pierre Vanhove

Preprint number: UUITP-25/18

We outline the program to apply modern quantum field theory methods to calculate observables in classical general relativity through a truncation to classical terms of the multi-graviton two-body on-shell scattering amplitudes between massive fields. Since only long-distance interactions corresponding to non-analytic pieces need to be included, unitarity cuts provide substantial simplifications for both post-Newtonian and post-Minkowskian expansions. We illustrate this quantum field theoretic approach to classical general relativity by computing the interaction potentials to second order in the post-Newtonian expansion, as well as the scattering functions for two massive objects to second order in the post-Minkowskian expansion. We also derive an all-order exact result for gravitational light-by-light scattering.

Unraveling conformal gravity amplitudes

Calabi-Yau Manifolds and SU (3) Structure

Authors: Magdalena Larfors, Andre Lukas, Fabian Ruehle

Preprint number: UUITP-23/18

On the universality of late-time correlators in semi-classical 2d CFTs

Authors: Souvik Banerjee, Jan-Willem Bryan, Gideon Vos

Preprint number: UUITP-22/18

The Analytic Bootstrap for Large N Chern-Simons Vector Models

Authors: Ofer Aharony, Luis F. Alday, Agnese Bissi, Ran Yacoby

Preprint number: UUITP-21/18

Three-dimensional Chern-Simons vector models display an approximate higher spin symmetry in the large N limit. Their single-trace operators consist of a tower of weakly broken currents, as well as a scalar σ of approximate twist 1 or 2. We study the consequences of crossing symmetry for the four-point correlator of σ in a 1/N expansion, using analytic bootstrap techniques. To order 1/N we show that crossing symmetry fixes the contribution from the tower of currents, providing an alternative derivation of well-known results by Maldacena and Zhiboedov. When σ has twist 1 its OPE receives a contribution from the exchange of σ itself with an arbitrary coefficient, due to the existence of a marginal sextic coupling. We develop the machinery to determine the corrections to the OPE data of double-trace operators due to this, and to similar exchanges. This in turns allows us to fix completely the correlator up to three known truncated solutions to crossing. We then proceed to study the problem to order 1/N^2. We find that crossing implies the appearance of odd-twist double-trace operators, and calculate their OPE coefficients in a large spin expansion. Also, surprisingly, crossing at order 1/N^2, implies non-trivial O(1/N) anomalous dimensions for even-twist double-trace operators, even though such contributions do not appear in the four-point function at order 1/N (in the case where there is no scalar exchange). We argue that this phenomenon arises due to operator mixing. Finally, we analyse the bosonic vector model with a sextic coupling without gauge interactions, and determine the order 1/N^2 corrections to the dimensions of twist-2 double-trace operators.

Complete integration-by-parts reductions of the non-planar hexagon-box via module intersections

Authors: Janko Böhm, Alessandro Georgoudis, Kasper J. Larsen, Hans Schönemann, Yang Zhang

Preprint number: UUITP-16/18

We present the powerful module-intersection integration-by-parts (IBP) method,
for multi-loop Feynman integral reduction. With modern computational algebraic geome-
try techniques, this new method manages to trim traditional IBP systems dramatically to
much simpler integral-relation systems on unitarity cuts. We demonstrate the power of this method by the complete analytic reduction of two-loop five-point non-planar hexagon-box integrals, with degree-four numerators, to the 73 master integrals.

A massive class of N= 2 AdS(4) IIA solutions

Authors: Achilleas Passias, Daniel Prins, Alessandro Tomasiello

Preprint number: UUITP-20/18

We initiate a classification of N=2  supersymmetric AdS(4) solutions of (massive) type IIA supergravity. The internal space is locally equipped with either an SU(2) or an identity structure. We focus on the SU(2) structure and determine the conditions it satisfies, dictated by supersymmetry. Imposing as an ansatz that the internal space is complex, we reduce the problem of finding solutions to a Riccati ODE, which we solve analytically. We obtain in this fashion a large number of new families of solutions, both regular as well as with localized O8-planes and conical Calabi-Yau singularities. We also recover many solutions already discussed in the literature.
 

AdS Weight Shifting Operators

Authors: Miguel S. Costa and Tobias Hansen

Preprint number: UUITP-19/18

We construct a new class of differential operators that naturally act on AdS harmonic functions. These are weight shifting operators that change the spin and dimension of AdS representations. Together with CFT weight shifting operators, the new operators obey crossing equations that relate distinct representations of the conformal group. We apply our findings to the computation of Witten diagrams, focusing on the particular case of cubic interactions and on massive, symmetric and traceless fields. In particular we show that tree level 4-point Witten diagrams with arbitrary spins, both in the external fields and in the exchanged field, can be reduced to the action of weight shifting operators on similar 4-point Witten diagrams where all fields are scalars. We also show how to obtain the conformal partial wave expansion of these diagrams using the new set of operators. In the case of 1-loop diagrams with cubic couplings we show how to reduce them to similar 1-loop diagrams with scalar fields except for a single external spinning field (which must be a scalar in the case of a two-point diagram). As a bonus, we provide new CFT and AdS weight shifting operators for mixed-symmetry tensors.

Perturbing AdS(6) x S(4): linearised equations and spin-2 spectrum

Authors: Achilleas Passias and Paul Richmond

Preprint number: UUITP-18/18

We initiate the analysis of the Kaluza--Klein mass spectrum of massive IIA supergravity on the warped AdS(6) x S(4) background, by deriving the linearised equations of motion of bosonic and fermionic fluctuations, and determining the mass spectrum of those of spin-2. The spin-2 modes are given in terms of hypergeometric functions and a careful analysis of their boundary conditions uncovers the existence of two branches of mass spectra, bounded from below. The modes that saturate the bounds belong to short multiplets which we identify in the representation theory of the f(4) symmetry superalgebra of the AdS(6) x S(4) solution.

One-point functions in β-deformed N = 4 SYM with defect

Author: Erik Widén   

Preprint number: UUITP-17/18

Precision matching of circular Wilson loops and strings in AdS(5)xS(5)

Authors: Daniel Medina-Rincon, Arkady A. Tseytlin and Konstantin Zarembo    

Preprint number: UUITP-15/18

Previous   attempts  to match the exact N=4  super Yang-Mills expression for the expectation value of the 1/2-BPS circular Wilson loop with the semiclassical AdS(5)xS(5) string theory prediction were not successful  at the first subleading order. There was a missing prefactor lambda^(-3/4) which could be attributed to the unknown normalization of the string path integral measure. Here we resolve this problem by computing, following arXiv:1712.07730, the ratio of the string partition functions corresponding to the circular Wilson loop and the special 1/4-supersymmetric latitude Wilson loop. The fact that the latter has a trivial expectation value in the gauge theory allows us to relate the prefactor to the contribution of the three zero modes  of the ``transverse" fluctuation operator in the 5-sphere directions.

Morita equivalence and the generalized Kähler potential

Preprint number: UUITP-14/18

Abstract: We solve the problem of determining the fundamental degrees of freedom underlying a generalized K\"ahler structure of symplectic type. For a usual K\"ahler structure, it is well-known that the geometry is determined by a complex structure, a K\"ahler class, and the choice of a positive (1,1)-form in this class, which depends locally on only a single real-valued function: the K\"ahler potential. Such a description for generalized K\"ahler geometry has been sought since it was discovered in 1984. We show that a generalized K\"ahler structure of symplectic type is determined by a pair of holomorphic Poisson manifolds, a holomorphic symplectic Morita equivalence between them, and the choice of a positive Lagrangian brane bisection, which depends locally on only a single real-valued function, which we call the generalized K\"ahler potential. Our solution draws upon, and specializes to, the many results in the physics literature which solve the problem under the assumption (which we do not make) that the Poisson structures involved have constant rank. To solve the problem we make use of, and generalize, two main tools: the first is the notion of symplectic Morita equivalence, developed by Weinstein and Xu to study Poisson manifolds; the second is Donaldson's interpretation of a K\"ahler metric as a real Lagrangian submanifold in a deformation of the holomorphic cotangent bundle.