Wednesday Seminars

Some of the seminars take place remotely on Zoom. If you would like to attend via Zoom but have not subscribed to the mailing list yet you can contact the organizers in order to obtain the passcode.

In addition to the Wednesday seminars there is a biweekly Nordic remote HET seminar.

Organizers: Kays HaddadJacopo Sisti

Fall 2022

Marko Berghoff (HU Berlin)

07 December 2022, 13.45

Location: Å80109

Title: The geometry of scattering amplitudes

Abstract: Scattering amplitudes can be studied from many viewpoints, connecting them with (a priori) very different areas of mathematics. One example is the work of Bloch, Brown, Esnault, Kreimer (and others) who uncovered the (algebraic) geometry behind Feynman periods. Generalizing this approach to Feynman amplitudes poses some serious difficulties, as then the geometry depends on parameters (kinematics): Instead of single periods, we now need to understand families of periods, or rather the respective geometries. While the complete answer remains a mystery, a lot of information can already be gained from studying where and how the geometry degenerates. This "singularity theory" approach allows to determine the poles and branch points of amplitudes (the Landau variety) and make some qualitative statements about their nature. In particular, it produces vanishing criteria for iterated variations (eg (extended) Steinmann relations). This is joint work with Erik Panzer (U Oxford).

Ling Lin (Oxford)

30 November 2022, 13.45

Location: Å4003

Title: Aspects of decomposition

Abstract: A d-dimensional quantum field theory with (d-1)-form symmetry is conjectured to “decompose” into individual quantum field theories. After a review of this phenomenon, I will discuss two instances where decomposition occurs in a subtle way: the fusion rules of condensation defects in 3d gauge theories, and in string / M-theory compactifications with frozen singularities.

Alfredo Guevara (Harvard)

Thu 24 November 2022, 15.15

Location: Å80121

Title: Gravity amplitudes, W_{1+\inf} and color-kinematics

Abstract: W-algebras are ubiquitous extended symmetries of a vast class of CFTs, with deep connections to quantum groups and integrability. Recently, through the techniques of celestial holography, the W_{1+inf} algebra was realized explicitly in celestial correlation functions associated to 4d gravitational scattering amplitudes, but the connection to other realizations of the symmetry, and in particular integrability, was vaguely understood. In this talk I will attempt to shed some light on this issue, arguing that the emergence of the symmetry is directly connected to the color-kinematics duality relating gravity and gauge theory amplitudes, at the same time unveiling an associative structure in collinear singularities of the tree-level S-Matrix.

Giulio Salvatori (Brown U.)

02 November 2022, 13.45

Location: Å80109

Title: Positive Geometries and Scattering Amplitudes

Abstract: In recent years it has been appreciated how the physics of scattering amplitudes can be described in terms of Positive Geometry. While this was first understood in the context of scattering in maximally super symmetric Yang-Mills theory, whose planar S-matrix is tied to a geometry called Amplituhedron, recent developments have shown how a positive geometric picture holds more generally: bosonic string theory, non supersymmetric field theories beyond the planar limit and even individual Feynman diagrams all admit a geometry describing some of their most salient features. In my talk I will review these recent developments in a self contained fashion, without assuming any prior knowledge on the topic.

Alessandro Pini (Turin U.)

Thu 13 October 2022, 13.45

Location: Zoom

Title: Localization vs holography in some 4d N=2 SCFTs

Abstract: We analyse two distinct 4d N=2 SCFTs. The first theory has gauge group SU(N) and matter in the symmetric plus anti-symmetric representation. The second is a quiver gauge theory obtained with an orbifold projection from N=4 SYM. For both theories we compute the 2-point and 3-point correlation functions among chiral/anti-chiral single trace operators and the corresponding structure constants. In the first part of the seminar, using supersymmetric localization, we map the computation to an interacting matrix model and obtain expressions for the structure constants that are valid for any value of the 't Hooft coupling in the planar limit of the theory. In particular, at strong coupling, these expressions simplify and allow us to extract the leading behaviour in an analytic way. We successfully compare these predictions to a direct Monte Carlo numerical evaluation of the matrix integral and to Padé resummation derived from very long perturbative series. Finally, using the AdS/CFT correspondence, we compute the structure constants from the dual supergravity theory and obtain results that perfectly match the strong-coupling predictions from localization.

Anindita Maiti (IAIFI, Cambridge U.)

05 October 2022, 13.45

Location: Zoom

Title: A Study of Neural Network Field Theories

Abstract: The backbones of modern-day Deep Learning, Neural Networks (NN), define field theories on Euclidean background through their architectures, where field interaction strengths depend on the choice of NN architecture width and stochastic parameters. Infinite width limit of NN architectures, combined with independently distributed stochastic parameters, lead to generalized free field theories by the Central Limit Theorem (CLT). Small and large deviations from the CLT, due to finite architecture width and/or correlated stochastic parameters, respectively give rise to weakly coupled field theories and non-perturbative non-Lagrangian field theories in Neural Networks. I will present a systematic exploration of Neural Network field theories via a dual framework of NN parameters: non-Gaussianity, locality by cluster decomposition, and symmetries are studied without necessitating the knowledge of an action. Such a dual description to statistical or quantum field theories in Neural Networks can have potential implications for physics.

Fridrik Gautason (Iceland U.)

28 September 2022, 13.45

Location: Å80127

Title: Wilson loops and non-conformal Holography

Abstract: I will discuss two examples of non-conformal holographic theories. First is the maximally supersymmetric Yang-Mills theory in five dimensions, and the second is a mass deformation of N=4 SYM in four dimensions commonly known as N=2^*. Using supersymmetric localization, the expectation value of  BPS Wilson loop operator can be computed exactly at large rank and strong coupling in both of these theories. In the talk I will review these results and explain how to reproduce them in string theory.

Martin Cederwall (Gothenburg U.)

21 September 2022, 13.45

Location: Å80101

Title: Supersymmetry and Koszul duality

Abstract: Pure spinor superfield theory provides a way to describe essentially any supermultiplet as the cohomology of a nilpotent operator Q=\lambda^\alpha D_\alpha, the contraction of a spinorial covariant superspace derivative with a spinor, which is constrained to obey (\lambda\gamma^a\lambda)=0. I will give a very brief review of how this comes about, and how it can be used to obtain Batalin-Vilkovisky actions for D=10 super-Yang-Mills theory and D=11 supergravity with manifest supersymmetry. Then I will talk about the constrained object \lambda itself, in particular how the very simple quadratic constraint (without any reference to space-time) encodes the full information about the supermultiplet in question. The tool used is the Koszul dual superalgebra – in an appropriate sense, which I will explain – to the associative algebra generated by \lambda. I will maybe also comment on some future prospects and applications. This is work in progress in collaboration with S. Jonsson, J. Palmkvist and I. Saberi.

Ulf Lindström (Middle East Tech. U., Ankara and Uppsala U.)

Tue 20 September 2022, 15.15

Location: Å80109

Title: Yano F-structures and extended supersymmetry

Abstract: Extended supersymmetry realised directly on the (2,2) semichiral superfields of a symplectic sigma model gives rise to a geometry on the doubled tangent bundle consisting of two Yano F structures on an almost para-hermitian manifold. Closure of the algebra and invariance of the action is discussed in this framework and integrability of the F structures is defined and shown to hold. The reduction to the usual (1, 1) sigma model description and identification with the bi-quaternionic set of complex structures and their properties is elucidated.

Victor Pozsgay (Imperial College)

Mon 12 September 2022, 13.45

Location: Å101166

Title: Low-energy EFT causality bounds

Abstract: In this talk, I will present a new tool to constrain low-energy Wilson coefficients in a scalar EFT (scalar for simplicity's sake but the range of applicability is much wider) based on the requirement that such theories should respect causality. Causality will be defined in the sense that no low-energy observer should be able to measure any resolvable time-advance resulting from a scattering event. I will show that these so-called causality bounds are in remarkable agreement with previously derived positivity bounds (where low energy constraints on the 4-point amplitude make use of physical assumptions of the UV completion of the EFT), while being considerably simpler and a better candidate to get cosmological and black hole gravitational bounds.

Felipe Diaz-Jaramillo (Humbolt U.)

7 September 2022, 15.15

Location: Å80127

Title: Double field theory as the double copy of Yang-Mills theory

Abstract: The Bern-Carrasco-Johansson (BCJ) double copy in scattering amplitudes states that exchanging colour information by kinematic information in Yang-Mills (YM) amplitudes leads to gravity amplitudes. In this talk, based on the BCJ double copy, I will establish a relation at the level of the action and gauge structure between YM and a reformulation of the Graviton-B-field-Dilaton theory on a doubled spacetime, called Double Field Theory (DFT). I will present two approaches to do this: the first one is a simple colour-kinematic substitution in the YM action that yields the gauge invariant action of DFT at quadratic order and a gauge-fixed version at cubic order. The second approach is based on Lie homotopy algebras. These mathematical structures encode field theories including their symmetries and, in particular, the algebra of YM exhibits a manifest colour-kinematic split. I will show that, in the spirit of the BCJ construction, replacing colour by kinematics at this algebraic level reproduces the gauge invariant DFT action up to cubic order.

Spring 2022

Mauricio Romo (Tsinghua U.)

Thu 18 August 2022, 13.45

Location: Å90101

Title: GLSM, Homological projective duality and nc resolutions

Abstract: Kuznetsov's Homological projective duality (HPD) in algebraic geometry is a powerful theorem that allows to extract information about semiorthogonal decompositions of derived categories of certain varieties. I will review it and give a GLSMs perspective based on categories of B-branes. I will focus mostly on the case of Fano (hypersurfaces) manifolds. In general, for such cases the HPD can be interpreted as a non-commutative (nc) resolution of a compact variety. I will give a physical interpretation of this fact and present some conjectures.

Marcus Berg (Karlstad U.)

Mon 20 June 2022, 13.45

Location: Å90101

Title: One-loop N<max string amplitudes

Abstract: I will review some work in progress on field theory limits of one-loop four-point string amplitudes in less-than-maximal supersymmetry. This is a continuation of 1603.05262.

Marco David (ENS Paris & Uppsala U.)

08 June 2022, 13.45

Location: Å90101 or Zoom

Title: QED. The Quest to Formally Verify Mathematics

Abstract: Mathematics prides itself as the most fundamental of sciences, constructed as a pyramid of proven truths. Yet, the proof style of most mathematicians is strikingly different from an ideal, fully rigorous argument. At the same time, mathematical proofs are becoming increasingly sophisticated, stretching the boundaries of what is humanly comprehensible. Inevitably, mistakes will go unnoticed, putting the unique status of mathematics as exact science into peril. Now may be the time to reconcile the intuitive with the correct through the advent of “computer proof assistants”. For the most time, this has been a topic for experts in specialized communities. More recently, major theorems in mathematics have been computer-verified by people from outside of these communities, even by students. This talk presents a journey through the field of interactive theorem proving with particular emphasis on mathematics. Challenging well-known preconceptions and exploring new perspectives, we give an outlook on future applications, including in mathematical physics.

Mariana Carrillo Gonzalez (Imperial College)

01 June 2022, 13.45

Location: Å90101

Title: Constructing Massive Double Copies

Abstract: In this talk, I will give a short introduction to the double copy relation that gives gravity as the “square” of Yang-Mills. I will focus on explaining how to extend this relation to the case of massive mediators and explain the issues that arise in this situation. I will mention some standard ways of solving these issues as well as two novel theories that can have well-defined double copies. One consists of a cubic scalar with an additional infinite-dimensional symmetry and the other one consists of topologically massive theories. Time permitting, I will also mention a classical double copy relation that arises for the latter.

Vasco Gonçalves (Porto U.)

Thu 26 May 2022, 13.45

Location: Zoom

Title: The Wilson Loop – Large Spin OPE Dictionary

Abstract: In this talk I will work out the map between null polygonal hexagonal Wilson loops and spinning three point functions in large N conformal gauge theories by mapping the variables describing the two different physical quantities and by working out the precise normalization factors entering this duality. By fixing all the kinematics we open the ground for a precise study of the dynamics underlying these dualities – most notably through integrability in the case of planar maximally supersymmetric Yang-Mills theory.

Lionel Mason (Oxford U.)

25 May 2022, 13.45

Location: Å80121

Title: The twistor origin of hidden w-infinity symmetries in celestial gravity

Abstract: Recently in their celestial holography programme, Strominger and coworkers attempt to provide a holographic description of conventional 4d gravity. In their investigations, they uncovered a hidden w-infinity symmetry in their ‘celestial soft OPEs’ for graviton scattering. This talk will explain the origin of this symmetry in terms of old ideas of Newman and Penrose based on light-cone cuts of null infinity and their description in terms of asymptotic twistors and certain sigma models in asymptotic twistor space. Wn symmetries were introduced by Zamolodchikov as higher spin symmetries in 2d conformal field theories. These were given a geometric interpretation for n=infinity as area-preserving diffeomorphisms of the plane. I will explain how the corresponding loop algebra becomes a hidden symmetry of self-dual gravity via Penrose's nonlinear graviton construction. The action of this symmetry on the tree-level S-matrix of full gravity beyond the self-dual sector will then be obtained from its action on a sigma model in the asymptotic twistor space of a general space-time. This talk is based on 2110.06066 and 2103.16984.

Emil Bjerrum-Bohr (NBI)

18 May 2022, 15.15

Location: Å80121

Title: Binary Merger Dynamics from Scattering Amplitudes

Abstract: Gravity is a fundamental force but so weak that we have limited understanding of its extreme interactions. A recent exciting development is the detection of collisions of black holes in the Universe. These phenomena witnessed by the Laser Interferometer Gravitational-Wave Observatory (LIGO) have refreshed enthusiasm for exploration of gravitational interactions and stimulated critical advancement of precision analysis of merger events. We will in this talk outline how to derive dynamics in general relativity by application of modern on-shell amplitude techniques and discuss how such methods can complement existing technology and facilitate computational progress.

Davide Passaro (Amsterdam U.)

18 May 2022, 13.45

Location: Å80121

Title: 3-manifolds and VOAs through Ẑ invariants

Abstract: Q-series are a concise and elegant way of encoding physical and mathematical information into a single function. Examples of such q-series are the Ẑ 3-manifold invariants also known as homological blocks. Surprisingly Ẑ invariants appear in widely different areas throughout mathematics and physics, such as low dimensional topology and vertex operator algebras (VOA). The appearance of the Ẑ invariants in these two contexts originates from the unexpected number theoretical properties that Ẑ invariants have. In this talk I will discuss how the connection between 3-manifolds and  VOAs was established and how it has led to an increased understanding of the number theoretical aspects of Ẑ invariants.

Michelangelo Preti (King's College)

11 May 2022, 13.45

Location: Å80101

Title: Bootstrability in defect CFT

Abstract: We study how the exact non-perturbative integrability methods in 4D N = 4 Super-Yang-Mills can work efficiently together with the numerical conformal bootstrap techniques to go beyond the spectral observables and access previously unreachable quantities such as correlation functions at finite coupling. We consider the 1D defect CFT living on a 1/2-BPS Wilson line, whose non-perturbative spectrum is governed by the Quantum Spectral Curve (QSC). In addition, we use that the deformed setup of a cusped Wilson line is also controlled by the QSC. In terms of the defect CFT, this translates into two nontrivial relations connecting integrated 4-point correlators to cusp spectral data, such as the Bremsstrahlung and Curvature functions – known analytically from the QSC. Combining these new constraints and the spectrum of the 10 lowest-lying states with the Numerical Conformal Bootstrap, we obtain very sharp rigorous numerical bounds for the structure constants of the first non-protected states. Furthermore, we also develop analytic functional bootstrability obtaining weak coupling results for several structure constants.

Fabrizio Del Monte (Montreal U., CRM)

04 May 2022, 13.45

Location: Å4004

Title: Supersymmetric partition functions and isomonodromic tau functions

Abstract: Class S theories are four-dimensional N=2 QFTs that are obtained by wrapping M5-branes on Riemann surfaces with singular points. In recent years a correspondence between class S theories and isomonodromic deformations equations (whose simplest examples are the six Painlevé equations) is emerging, where the so-called isomonodromic tau function is identified with the dual partition function of the QFT. The tau functions can be typically written as Fredholm determinants or Pfaffians, providing a fully nonperturbative approach to study partition functions of class S theories, relying only on the geometric data entering in the string theory construction, and not on a classical action. After reviewing the Fredholm determinant formulation of tau functions for spheres with regular singularities, corresponding to linear quiver gauge theories, I will show how the description can be extended to tau functions with orthogonal gauge groups, that are written as Fredholm Pfaffians, and to tau functions for tori with regular singularities, corresponding to circular quiver gauge theories. I will conclude by showing how the tau function description allows to study the S-duality transformation of the resulting gauge theory dual partition function.

Anton Nedelin (Geneva U.)

27 April 2022, 13.45

Location: Å90101

Title: Integrable Models from N=1 Superconformal Indice

Abstract: In this talk I will present a method of derivation of previously known and new integrable finite difference operators using N=1 quantum field theories. I will start with brief review of the 4d compactifications of 6d SCFTs leading to the wide class of 4d SCFTs. Then I will show how to derive various finite difference operators using superconformal indices of this 4d theories as well as some intuition coming from the geometry of 6d compactifications. The talk is based on the preprint 2106.08335 as well as ongoing work in collaboration with Shlomo Razamat and Belal Nazzal.

Pietro Longhi (Uppsala U.)

20 April 2022, 13.45

Location: Å80115 or Zoom

Title: Instanton partition functions beyond weak coupling

Abstract: Localization provides a way to compute instanton partition functions of 4d N=2 QFTs by means of a Lagrangian description. The resulting expressions take the form of power series in the instanton counting parameters, and accordingly their range of validity is restricted to a neighbourhood of the weak-coupling regime where the series converges. I will review a proposal formulated in joint work with Coman and Teschner for the analytic continuation of 4d N=2 instanton partition functions beyond weak coupling, based on a relation to isomonodromic deformations of quantum Seiberg-Witten curves.

Raffaele Savelli (Rome U.)

06 April 2022, 13.45

Location: Å101136.B

Title: Computing OPE coefficients for Argyres-Douglas theories

Abstract: Argyres-Douglas theories are a special class of N=2 superconformal field theories in four dimensions, featuring an intrinsically strong dynamics. Due to the lack of a Lagrangian description, determining their properties quantitatively is a challenge. In this talk, I will present a general formula, which, inspired by the fact that such theories appear as saddle points of the sphere partition function of asymptotically-free gauge theories, computes, through localization techniques, the OPE coefficients between their Coulomb-Branch operators. The formula only depends on intrinsic data of the conformal field theory, that can be extracted from its Seiberg-Witten geometry. Although it neglects higher gravitational corrections, this formula gives results in surprising agreement with the bootstrap bounds. The talk is based on the work ArXiv:2112.11899, done in collaboration with A. Bissi, F. Fucito, A. Manenti, and F. Morales.

Alex Ochirov (Oxford U.)

30 March 2022, 13.45

Location: Å90101

Title: Classical scattering of spinning black holes from quantum amplitudes

Abstract: In view of the observations of gravitational-wave signals from black-hole mergers, classical black-hole scattering has received considerable interest due to its relation to the classical bound-state problem of two black holes inspiraling onto each other. In this talk I will discuss the link between classical scattering of spinning black holes and quantum scattering amplitudes for massive spin-s particles. I will derive the spin-exponentiated structure of the relevant tree-level amplitude from (in some sense) "minimal" coupling to Einstein's gravity, which in the s → ∞ limit generates the black holes' complete series of spin-induced multipoles. I will phrase this limit rigorously in the language of coherent-spin quantum states. Considering the first post-Minkowskian (PM) order, I will show how the resulting scattering function encodes in a simple way the classical net changes in the black-hole momenta and spins at 1PM order and to all orders in spins. I will then comment on the results and challenges at 2PM order and beyond.

Naveen Prabhakar

16 March 2022, 10.30

Location: Zoom

Title: A Hilbert space for large N Chern-Simons matter theories

Abstract: Chern-Simons theories in three dimensions coupled to vector-like matter are exactly solvable in the large N limit. This led to the discovery of ‘bosonisation’ in three dimensions wherein a Chern-Simons gauged fermion is dual to a Chern-Simons gauged boson with levels and ranks interchanged. The coupling of Chern-Simons gauge theory to bosons and fermions modifies the spin and the statistics of the matter excitations. Recently, the occupation number distribution of such Chern-Simons coupled matter was computed in the large N limit and was found to be a one-parameter interpolation between Fermi-Dirac and Bose-Einstein statistics. Subsequently, this modification of the statistics was understood in terms of an exclusion principle for bosons that arises due to the coupling to Chern-Simons gauge theory. In the talk, we will discuss these matters briefly and allude to possible future developments in this rich and fertile subject.

Johannes Walcher (Heidelberg U.)

09 March 2022, 13.45

Location: Zoom

Title: Irrationality of MUMs and extended mirror symmetry

Abstract: It was pointed out a while ago that the generic predictions of extended mirror symmetry depend on arithmetic data such as the field of definition of the algebraic cycle representing the D-brane in the B-model. Recently, we are exploring closed string analogues of this phenomenon in the guise of Calabi-Yau differential equations with points of maximal unipotent monodromy that are equally irrational. In my talk, I will explain the mathematical meaning and interest of these statements through examples, though we do not understand their physical interpretation.

Miroslav Rapčák (UC, Berkeley)

23 February 2022, 16.30

Location: Zoom

Title: Branes, BPS Algebras and COHA

Abstract: According to the famous AGT correspondence, there exists an action of the W_N algebra on the cohomology of the moduli space of instantons. This module admits an interpretation in terms of the space of vacua of a quantum mechanics describing the low energy dynamics of D0-branes bound to a stack of N D4-branes. The W_N algebra then captures processes of bounding and separating D0-branes from the stack. It is natural to ask if the story generalizes to D0-branes bound to intersecting branes and branes of different dimensions. In this talk, I will 1. Review the construction of the module structure using correspondences in algebraic geometry. 2. Illustrate the construction on the simplest example of D0-branes bound to a single D2-brane, recovering the vector representation of the gl_1 affine Yangian 3. Comment on some recent developments in the cohomological Hall algebra approach to the correspondence between branes and representation theory.

Rodolfo Panerai (Uppsala U.)

Tuesday 22 February 2022, 14.15 (Nordic HET)

Location: Zoom

Title: Exact TTbar-deformation of two-dimensional Yang-Mills theory

Abstract: In this talk, I will discuss the TTbar deformation of two-dimensional Yang-Mills theory on the sphere. Focusing on unitary gauge groups, I will show how the deformed partition function can be obtained by solving the relevant flow equation at the level of individual monopole sectors. For positive values of the deformation parameter, the quantum spectrum of the theory experiences a truncation, the partition function reducing to a sum over a finite set of energy states. For negative values, instead, the appearance of non-perturbative contributions drastically modifies the structure of the partition function, regularising its naive divergences and seemingly breaking locality. In the large-N expansion, the theory exhibits a rich phase diagram. The transitions between different phases are driven by instantons both in the 't Hooft coupling (leading to a deformed Douglas-Kazakov phase transition) and in the deformation parameter.

Niccolò Cribiori (Munich U., Max Planck Inst.)

16 February 2022, 13.45

Location: Zoom 658 2223 8569

Title: Open-Closed correspondence of K-theory and Cobordism

Abstract: Non-trivial K-theory groups and non-trivial cobordism groups can lead to global symmetries which are conjectured to be absent in quantum gravity. In this talk, a correspondence between the two groups is proposed. It is inspired by open-closed string duality and relies on a mathematical result known as Conner-Floyd isomorphism. As an application, it is shown how to recover known tadpole cancellation conditions of string theory from a purely bottom-up perspective. In the spirit of the swampland program, this can be used to give further support to the string lamppost principle.

Ingmar Saberi (Munich U.)

26 January 2022, 14.30

Location: Zoom 664 3233 5042

Title: Twisted eleven-dimensional supergravity and exceptional Lie superalgebras

Abstract: Twists of supersymmetric field theories have been the subject of intense and fruitful study for more than thirty years. Recently, there has been a great deal of progress on extending the technique of twisting to supergravity theories, building on the definition of twisted supergravity given by Costello and Li. Much of what is explicitly known about these theories comes from the topological B-model, whose string field theory, as studied by Bershadsky-Ceccotti-Ooguri-Vafa, conjecturally produces the holomorphic twist of type IIB supergravity. Progress on other supergravity theories, including eleven-dimensional supergravity, has been hindered by the lack of such a worldsheet approach. I will discuss a rigorous computation of the twist of the free eleven-dimensional supergravity multiplet, as well as an interacting BV theory with this field content that passes a large number of consistency checks. Surprisingly, the resulting holomorphic theory on flat space is closely related to the infinite-dimensional exceptional simple Lie superalgebra E(5,10). This is joint work with Surya Raghavendran and Brian Williams.

Francesco Aprile (Sao Paulo, IFT)

19 January 2022, 13.45

Location: Zoom

Title: Conformal blocks in diverse dimensions and the superconformal Cauchy identity

Abstract: I will describe 4pt conformal blocks for scalar operators in diverse dimensions by using a single unified formalism. I will discuss a property of the conformal blocks known as stability. This implies that when writing conformal blocks as certain multivariate series, the coefficients of this expansion only depend on Young diagrams. In particular, we can bosonise the conformal computation and simply focus on theories with compact groups. In this framework the blocks are polynomials of the BC root system after we apply complementation. I will then explain the connection with mathematics and show how to formulate a superconformal Cauchy identity which yields the CPW of any free theory diagram in any dimension. For discussion, I will finally mention q-deformations results in our framework.

Last modified: 2022-12-05