Preprints 2023

Authors: Carlos Rodriguez, Oliver Schlotterer and Yong Zhang

Preprint number: UUITP-26/23

One-loop scattering amplitudes in string theories involve configuration-space integrals over genus-one surfaces with coefficients of Kronecker-Eisenstein series in the integrand. A conjectural genus-one basis of integrands under Fay identities and integration by parts was recently constructed out of chains of Kronecker-Eisenstein series. In this work, we decompose a variety of more general genus-one integrands into the conjectural chain basis. The explicit form of the expansion coefficients is worked out for infinite families of cases where the Kronecker-Eisenstein series form cycles. Our results can be used to simplify multiparticle amplitudes in supersymmetric, heterotic and bosonic string theories and to investigate loop-level echoes of the field-theory double-copy structures of string tree-level amplitudes. The multitude of basis reductions in this work strongly validate the recently proposed chain basis and stimulate mathematical follow-up studies of more general configuration-space integrals with additional marked points or at higher genus.

Authors: Sibasish Banerjee, Pietro Longhi and Mauricio Romo

Preprint number: UUITP-25/23

Abstract: A certain class of $A$-branes in mirrors of toric Calabi-Yau threefolds can
be described through the framework of foliations. This allows to develop an
explicit description of their moduli spaces based on a cell decomposition, with
strata of various dimensions glued together in a way that is dictated by
partial degenerations of the underlying special Lagrangian. Examples of
$A$-branes associated with `wild' BPS states are considered in detail. The
torus fixed points in their moduli spaces provide a decomposition of $m$-herds
spectral networks into a number $|\Omega|$ of basic connected objects, where
$\Omega$ is the the corresponding rank-zero Donaldson-Thomas (DT) invariant. A
relation between the surgery parameters of the special Lagrangian and the
baryonic semi-invariants of the representation theory of $m$-Kronecker quivers
is also discussed, providing a local map between moduli spaces of branes
related by homological mirror symmetry.

Authors: Ulf Lindström 

Preprint number: UUITP-24/23

In this paper we look at a sigma model based on the (4, 4) twisted chiral multiplet [3]. It admits two geometric descriptions: The ususal biquater nionic geometry on the tangent space and a new geometry involving two Yano F-structures on a doubled tangent space. This analysis sheds light on the recent discussion of semichiral models in [1] and on an upcoming discus- sion of complex linears. 

Authors: Michele Del Zotto, Marco Fazzi, Suvendu Giri

Preprint number: UUITP-23/23

Abstract: We settle a long-standing question about the hypermultiplet moduli spaces of the heterotic strings on ALE singularities. These heterotic backgrounds are specified by the singularity type, an instanton number, and a (nontrivial) flat connection at infinity. Building on their interpretation as six-dimensional theories, we determine a class of three-dimensional N=4 quiver gauge theories whose quantum corrected Coulomb branch coincides with the exact heterotic hypermultiplet moduli space.

Author: Carlo Heissenberg

Preprint number: UUITP-22/23

We calculate the spin-orbit corrections to the loss of angular momentum in a two-body scattering at third Post-Minkowskian order, O(G^3), from scattering amplitudes using the eikonal operator. These results include effects linear in spin, are valid for generic spin orientations and are presented in a manifestly Poincaré covariant way. We include both  radiative losses, by means of the leading-order gravitational waveform, and static losses by means of the appropriate -i0 prescription in the leading soft graviton theorem, finding agreement with known results in the Post-Newtonian limit.

Authors: Eric D'Hoker, Martijn Hidding and Oliver Schlotterer

Preprint number: UUITP-21/23

Abstract: A wealth of information on multiloop string amplitudes is encoded in two-point functions of worldsheet fermions known as Szegö kernels. Cyclic products of an arbitrary number of Szegö kernels for any even spin structure $\delta$ on a Riemann surface of arbitrary genus are decomposed into linear combinations of modular tensors on moduli space that carry all the dependence on the spin structure $\delta$. The coefficients in these linear combinations are independent of $\delta$, carry all the dependence on the marked points and are composed of the integration kernels of higher-genus polylogarithms constructed in arXiv:2306.08644. The conditions under which these modular tensors are locally holomorphic on moduli space are determined and explicit formulas for the special case of genus two are presented.

Authors: Andrea Campoleoni, Arnaud Delfante, Dario Francia, Carlo Heissenberg

Preprint number: UUITP-20/23

We study the renormalized action and the renormalized presymplectic potential for Maxwell fields on Anti de Sitter backgrounds of any dimensions. We then use these results to explicitly derive finite boundary charges for angle-dependent asymptotic symmetries. We consider both Poincar\'e and Bondi coordinates, the former allowing us to control the systematics for arbitrary $D$, the latter being better suited for a smooth flat limit.

Authors: Fabrizio Del Monte, Pietro Longhi

Preprint number: UUITP-19/23

We show that TBA equations defined by the BPS spectrum of $5d$ $\CN=1$ $SU(2)$ Yang-Mills on $S^1\times \IR^4$ encode the q-Painlev\'e III$_3$ equation.
We find a fine-tuned stratum in the physical moduli space of the theory where solutions to TBA equations can be obtained exactly, and verify that they agree with the algebraic solutions to q-Painlev\'e. 
Switching from the physical moduli space to that of stability conditions, we identify two one-parameter deformations of the fine-tuned stratum, where 
the general solution of the q-Painlev\'e equation in 
terms of dual instanton partition functions continues to provide explicit TBA solutions.
Motivated by these observations, we propose a further extensions of the range of validity of this correspondence, under a suitable identification of moduli. 
As further checks of our proposal, we study the behavior of exact WKB quantum periods for the quantum curve of local $\mathbb{P}^1\times\mathbb{P}^1$.

Authors: Luca Cassia, Pietro Longhi, Maxim Zabzine

Preprint number: UUITP-18/23

Abstract: This paper introduces a concrete relation between genus zero closed Gromov-Witten invariants of Calabi-Yau threefolds and genus zero open Gromov-Witten invariants of a Lagrangian A-brane in the same threefold. Symplectic cutting is a natural operation that decomposes a symplectic manifold (X,ω) with a Hamiltonian U(1) action into two pieces glued along the invariant divisor. In this paper we study a quantum uplift of the cut construction defined in terms of equivariant gauged linear sigma models. The nexus between closed and open Gromov-Witten invariants is a quantum Lebesgue measure associated to a choice of cut, that we introduce and study. Integration of this measure recovers the equivariant quantum volume of the whole CY3, thereby encoding closed GW invariants. Conversely, the monodromies of the quantum measure around cycles in Kähler moduli space encode open GW invariants of a Lagrangian A-brane associated to the cut. Both in the closed and the open string sector we find a remarkable interplay between worldsheet instantons and semiclassical volumes regularized by equivariance. This leads to equivariant generating functions of GW invariants that extend smoothly across the entire moduli space, and which provide a unifying description of standard GW potentials. The latter are recovered in the non-equivariant limit in each of the different phases of the geometry.

Authors: Eric D'Hoker,  Martijn Hidding, and Oliver Schlotterer

Preprint number: UUITP-17/23

An explicit construction is presented of homotopy-invariant iterated integrals on a Riemann surface of arbitrary genus in terms of a flat connection valued in a freely generated Lie algebra. Our construction generalizes the generating series of elliptic polylogarithms in the work of Brown and Levin and thereby leads to a concrete proposal for polylogarithms at higher genus. The integration kernels are built from convolutions of the Arakelov Green function and its derivatives with holomorphic Abelian differentials, combined into a flat connection.

Authors: Paolo Di Vecchia, Carlo Heissenberg, Rodolfo Russo, Gabriele Veneziano

Preprint number: UUITP-14/23

Motivated by conceptual problems in quantum theories of gravity, the gravitational eikonal approach, inspired by its electromagnetic predecessor, has been successfully applied to the transplanckian energy collisions of elementary particles and strings since the late eighties, and to string-brane collisions in the past decade. After the direct detection of gravitational waves from black-hole mergers, most of the attention has shifted towards adapting these methods to the physics of black-hole encounters. For such systems, the eikonal exponentiation provides an amplitude-based approach to calculate classical gravitational observables, thus complementing more traditional analytic methods such as the post-Newtonian expansion, the worldline formalism, or the Effective-One-Body approach.
In this review we summarize the main ideas and techniques behind the gravitational eikonal formalism. We discuss how it can be applied in various different physical setups involving particles, strings and branes and then we mainly concentrate on the most recent developments, focusing on massive scalars minimally coupled to gravity, for which we aim at being as self-contained and comprehensive as possible.

Authors: Maor Ben-Shahar, Max Guillen

Preprint number: UUITP-13/23

11D pure spinors have been shown to successfully describe 11D supergravity in a manifestly super-Poincare covariant manner. The feasibility of its actual usage for scattering amplitude computations requires an efficient manipulation of the superfields defining linearized 11D supergravity. In this paper, we directly address this problem by finding the superspace expansions of these superfields, at all orders in θ, from recursive relations their equations of motion obey in Harnad-Shnider-like gauges. After introducing the 11D analogue of the 10D ABC superparticle, we construct, for the first time, a fully covariant vertex operator for 11D supergravity by making use of the linearized 11D superfields. Notably, we show that this vertex reproduces the Green-Gutperle-Kwon 11D operators in light-cone gauge.

Authors: Jim Lundin, Roman Mauch, Lorenzo Ruggeri

Preprint number: UUITP-12/23

Abstract: We compute the Coulomb branch partition function of the 4d N=2 vector multiplet on closed simply-connected quasi-toric manifolds B. This includes a large class of theories, localising to either instantons or anti-instantons at the torus fixed points (including Donaldson-Witten and Pestun-like theories as examples). The main difficulty is obtaining flux contributions from the localisation procedure. We achieve this by taking a detour via the 5d N=1 vector multiplet on closed simply-connected toric Sasaki-manifolds M which are principal S¹-bundles over B. The perturbative partition function can be expressed as a product over slices of the toric cone. By taking finite quotients M/Z_h along the S¹, the locus picks up non-trivial flat connections which, in the limit $h\to\infty$, provide the sought-after fluxes on B. We compute the one-loop partition functions around each topological sector on M/Z_h and B explicitly, and then factorise them into contributions from the torus fixed points. This enables us to also write down the conjectured instanton part of the partition function on B.

Authors: Michele Del Zotto, Marco Fazzi, Suvendu Giri

Preprint number: UUITP-11/23

Abstract: We begin a study the Higgs branches of the six-dimensional (1,0) little string theories (LSTs) governing the worldvolumes of heterotic ALE instantons. We give a description of such spaces by constructing the corresponding magnetic quivers. The latter are three-dimensional N=4 quiver gauge theories that flow in the infrared to 3d fixed points whose quantum corrected Coulomb branches are the Higgs branches of the six-dimensional theories of interest. We present results for both types of Heterotic strings, and mostly for C²/Z_k ALE spaces. Our analysis is valid both in the absence and in the presence of small instantons. Along the way, we also describe small SO(32) instanton transitions in terms of the corresponding magnetic quivers, which parallels a similar treatment of the small instanton transitions in the context of the E₈× E₈ heterotic string.

Authors: Rafael Aoude, Kays Haddad, Andreas Helset

Preprint number: UUITP-10/23

Abstract: We calculate the scattering of two rotating objects with the linear-in-curvature spin-induced multipoles of Kerr black holes at O(G²) and all orders in the spins of both objects. This is done including the complete set of contact terms potentially relevant to Kerr-black-hole scattering at O(G²). As such, Kerr black holes should be described by this scattering amplitude for a specific choice of values for the contact-term coefficients. The inclusion of all potential contact terms means this amplitude allows for a comprehensive search for structures emerging for certain values of the coefficients, and hence special properties that might be exhibited by Kerr-black-hole scattering. Our result can also act as a template for comparison for future computations of classical gravitational high-spin scattering.

Author: Alexander Söderberg Rousu

Preprint number: UUITP-09/23

We study fusion of two scalar Wilson defects. We propose that fusion holds at a quantum level by showing that bare one-point functions stay invariant. This is an expected result as the path integral stays invariant under fusion of the two defects. The difference instead lies in renormalization of local quantities on the defects. Those on the fused defect takes into account UV divergences in the fusion limit when the two defects approach eachother, in addition to UV divergences in the coincident limit of defect-local fields and in the near defect limits of bulk-local fields. At the fixed point of the corresponding RG flow the two conformal defects have fused into a single conformal defect.

Author: Alexander Söderberg Rousu

Preprint number: UUITP-08/23

Replica twist defects are of codimension two and enter in quantum information when finding the Rényi entropy. In particular, they generate n replicas of the bulk conformal field theory. We study the monodromy of such defect and learn how a global O(N)-symmetry is broken. By applying the equation of motion to the bulk-defect operator-product expansion we are able to extract the anomalous dimension of defect-local fields.

Authors: Bobby Samir Acharya, Michele Del Zotto, Jonathan J. Heckman, Max Hubner, Ethan Torres

Preprint number: UUITP-07/23

One of the general strategies for realizing a wide class of interacting QFTs is via junctions and intersections of higher-dimensional bulk theories. In the context of string/M-theory, this includes many D>4 superconformal field theories (SCFTs) coupled to an IR free bulk. Gauging the flavor symmetries of these theories and allowing position dependent gauge couplings provides a general strategy for realizing novel higher-dimensional junctions of theories coupled to localized edge modes. Here, we show that M-theory on singular, asymptotically conical G(2)-holonomy orbifolds provides a general template for realizing strongly coupled 5D bulk theories with 4D N=1 edge modes. This geometric approach also shows how bulk generalized symmetries are inherited in the boundary system.

Author: Alexander Söderberg Rousu

Preprint number: UUITP-06/23

We study the $\phi^6 - \hat{\phi}^4$ model with $O(N)$-symmetry near three dimensions. This model has a sextic bulk-interaction and a quartic boundary-interaction. The bulk two-point correlator is found upto two-loops by solving the equation of motion and applying the boundary conditions. Finally we apply the Coleman-Weinberg mechanism to this model, which allows us to flow along the renormalization group to a first-ordered phase transition. At one-loop order only the boundary receives a non-trivial effective potential, giving the scalar on the boundary a vacuum expecation value. However, due to the boundary operator product expansion, the bulk one-point function is non-zero as well. This leads to a spontaneous symmetry breaking of the original $O(N)$-symmetry.

Author: Jian Qiu

Preprint number: UUITP-05/23

Abstract: The ‘brane quantisation’ procedure is developed by Gukov and Witten [GW09]. We implement this idea by combining it with the tilting theory and the minimal resolutions. This way, we can realistically compute the deformation quantisation on the space of observables acting on the Hilbert space. We apply this procedure to the quantisation problem of generalised Kähler structure on P 2. Our approach differs from and complements that of Bischoff and Gualtieri [BG22]. We also benefitted from an important technical tool: a combinatorial criterion for the Maurer-Cartan equation, developed in [BW20] by Barmeier and Wang.

Author: Alexander Söderberg Rousu

Preprint number: UUITP-04/23

We consider a conformal field theory in the presence of a boundary, and explain how two-point correlators of mixed bulk-local operators can be bootstrapped by exploiting the analytical structure of the conformal blocks. This yields the operator product expansion coefficients in either bootstrap channel. We apply this bootstrap technique to an $O(N)$-model in $d = 4 - \epsilon$ dimensions to find the $\phi - \phi^5$ bulk correlator and the corresponding operator product expansion coefficients upto $\mathcal{O}(\epsilon)$.

Parts of this paper was first presented in my thesis.

Authors: Alessandro Georgoudis, Carlo Heissenberg, Ingrid Vazquez-Holm

Preprint number: UUITP-03/23

Abstract: We calculate the inelastic $2\to3$ one-loop amplitude for the scattering of two point-like, spinless objects with generic masses involving the additional emission of a single graviton. We focus on the near-forward, or classical, limit. Our results include the leading and subleading orders in the soft-region expansion, which captures all non-analytic contributions in the transferred momentum and in the graviton's frequency. This allows us to check the first constraint arising from the inelastic exponentiation put forward in Refs. 2107.12891, 2112.07556, 2210.12118 and to calculate the $2\to3$ one-loop matrix element of the $N$-operator, linked to the $S$-matrix by $S = e^{iN}$, showing that it is real, classical and free of infrared divergences.
We discuss how our results feature in the calculation of the $\mathcal O(G^3)$ corrections to the asymptotic waveform.

Authors: Kays Haddad

Preprint Number: UUITP-02/23

We study the compatibility of recursive techniques with the classical limit of scattering amplitudes through the construction of the classical Compton amplitude for general spinning compact objects. This is done using BCFW recursion on three-point amplitudes expressed in terms of the classical spin vector and tensor, and expanded to next-to-leading-order in $\hbar$ by using the heavy on-shell spinors. Matching to the result of classical computations, we find that lower-point quantum contributions are, in general, required for the recursive construction of classical, spinning, higher-point amplitudes with massive propagators. We are thus led to conclude that BCFW recursion and the classical limit do not commute. In possession of the classical Compton amplitude, we remove non-localities to all orders in spin for opposite graviton helicities, and to fifth order in the same-helicity case. Finally, all possible on-shell contact terms potentially relevant to black-hole scattering at the second post-Minkowskian order are enumerated and written explicitly.

Authors: Okan Günel, Ulf Lindström and Özgür Sarioğlu

Preprint number: UUITP-01/23

We construct an asymptotic conserved charge for a current that has been defined using Killing-Yano tensors. We then calculate the corresponding conserved charges of of the Kerr and AdS-Kerr black holes, and their higher-dimensional generalizations, Myers-Perry and Gibbons-Lu ̈-Page-Pope black holes. The new charges all turn out to be proportional to the angular momenta of their parent black holes.