# “Strings, CFT & Integrability”

## Spring Semester 2020

Wednesday, 11:45, zoom: 301-229-497

Organised by: Niklas Beisert, Matthias Gaberdiel, Daniel Medina, Hagen Münkler

day

date

date

time

venue

venue

speaker

title

title

Wed

25.03.

15:30

zoom: 301-229-497

Scott Collier (Harvard University)

“Virasoro analytic bootstrap and universal dynamics in CFT₂”

Wed

01.04.

11:45

zoom: 301-229-497

Carlo Heissenberg (Nordita)

“Asymptotic symmetries: higher spins and higher dimensions”

abstract (click to view)
The interplay between asymptotic symmetries and their observable counterparts, soft theorems and memory effects, has recently drawn renewed attention on the asymptotic properties of gauge theories near null infinity. We present recent developments in the analysis of such properties for higher dimensions and for theories possessing fields with arbitrary integer spin. Our discussion is mainly motivated by the fact that Weinberg’s soft theorem holds for arbitrary spins and dimensions. In this context, we focus on the possibility of introducing infinite-dimensional asymptotic symmetries whose Ward identities give rise to the soft theorem, compatibly with the finiteness of physical observables at infinity, and residual symmetries which are suited to the interpretation of memory effects as vacuum transitions. (click to hide)

Wed

08.04.

11:45

zoom: 301-229-497

Evgeny Sobko (Southampton University)

“Large N and Double-Scaling Limit in Principal Chiral Model: a New Non-Critical String?”

abstract (click to view)
I will present a systematic, non-perturbative analysis of the

two-dimensional SU(N) Principal Chiral Model (PCM) in the large-N limit.

Starting with the known infinite-N solution for the ground state at fixed

chemical potential, we devise an iterative procedure to solve the Bethe

ansatz equations order by order in 1/N. The first few orders, which are

explicitly computed, reveal a systematic enhancement pattern at strong

coupling calling for the near-threshold resummation of the large-N

expansion. The resulting double-scaling limit bears striking similarities

to the c=1 non-critical string theory and suggests that the double-scaled

PCM is dual to a non-critical string with a 2+1-dimensional target space

where an additional dimension emerges from the SU(N) Dynkin diagram. (click to hide)

two-dimensional SU(N) Principal Chiral Model (PCM) in the large-N limit.

Starting with the known infinite-N solution for the ground state at fixed

chemical potential, we devise an iterative procedure to solve the Bethe

ansatz equations order by order in 1/N. The first few orders, which are

explicitly computed, reveal a systematic enhancement pattern at strong

coupling calling for the near-threshold resummation of the large-N

expansion. The resulting double-scaling limit bears striking similarities

to the c=1 non-critical string theory and suggests that the double-scaled

PCM is dual to a non-critical string with a 2+1-dimensional target space

where an additional dimension emerges from the SU(N) Dynkin diagram. (click to hide)

Wed

15.04.

11:45

zoom: 301-229-497

Shouvik Datta (UCLA & ETH Zurich)

“Eigenstate thermalization and Virasoro symmetry”

abstract (click to view)
Two dimensional conformal field theories have an infinite number of

conserved charges and, at the same time, are dual to 3d gravity which

admits black hole solutions. This leads to a puzzle on how the

thermalization process can occur. We address universal aspects of this

question which can be leveraged by using Virasoro symmetry alone. It turns

out that matrix elements of light probes in typical high-energy descendant

states have the right properties to ensure compatibility with the weak

version of the Eigenstate Thermalization Hypothesis (ETH). The tools

developed along the way also enable us to directly prove the property of

conformal blocks exponentiating in the semi-classical regime. (click to hide)

conserved charges and, at the same time, are dual to 3d gravity which

admits black hole solutions. This leads to a puzzle on how the

thermalization process can occur. We address universal aspects of this

question which can be leveraged by using Virasoro symmetry alone. It turns

out that matrix elements of light probes in typical high-energy descendant

states have the right properties to ensure compatibility with the weak

version of the Eigenstate Thermalization Hypothesis (ETH). The tools

developed along the way also enable us to directly prove the property of

conformal blocks exponentiating in the semi-classical regime. (click to hide)

Wed

22.04.

10:45

zoom: 301-229-497

Ivan Kostov (CEA Saclay)

“The Octagon Form Factor in N=4 SYM”

abstract (click to view)
The computation of a certain class of four-point functions of heavily charged BPS operators boils down to the computation of a special form factor - the octagon - obtained by gluing together two hexagon form factors. The octagon represents an infinite sum over the mirror magnons circulating between the two hexagons. The sum resembles a Coulomb gas and can be repackaged as an expectation value in the Fock space of chiral fermions. This gives a representation of the octagon as a Fredholm pfaffian. Due to a doubling phenomenon the Fredholm pfaffian is in fact a Fredholm determinant. In this text I will review the main analytical techniques to handle this determinant, which allow to build systematically the weak and the strong coupling expansions of the octagon. The talk is based on the works [1–8]

References:

1. F. Coronado, “Bootstrapping the simplest correlator in planar N=4 SYM at all loops,”hep-th/1811.03282.

2. F. Coronado, “Perturbative four-point functions in planarN=4SYM from hexagonalization,”JHEP01(2019) 056,hep-th/1811.00467.

3. I. Kostov, V. B. Petkova, and D. Serban, “Determinant formula for the octagon form factor in N=4SYM,”1903.05038.

4. I. Kostov, V. B. Petkova, and D. Serban, “The Octagon as a Determinant,”1905.11467.

5. T. Bargheer, F. Coronado, and P. Vieira, “Octagons I: Combinatorics and Non-Planar Resummations,”1904.00965.

6. T. Bargheer, F. Coronado, and P. Vieira, “Octagons II: Strong Coupling,”1909.04077.

7. A. V. Belitsky and G. P. Korchemsky, “Exact null octagon,”1907.13131.

8. A. V. Belitsky and G. P. Korchemsky, “Octagon at finite coupling,”2003.01121. (click to hide)

References:

1. F. Coronado, “Bootstrapping the simplest correlator in planar N=4 SYM at all loops,”hep-th/1811.03282.

2. F. Coronado, “Perturbative four-point functions in planarN=4SYM from hexagonalization,”JHEP01(2019) 056,hep-th/1811.00467.

3. I. Kostov, V. B. Petkova, and D. Serban, “Determinant formula for the octagon form factor in N=4SYM,”1903.05038.

4. I. Kostov, V. B. Petkova, and D. Serban, “The Octagon as a Determinant,”1905.11467.

5. T. Bargheer, F. Coronado, and P. Vieira, “Octagons I: Combinatorics and Non-Planar Resummations,”1904.00965.

6. T. Bargheer, F. Coronado, and P. Vieira, “Octagons II: Strong Coupling,”1909.04077.

7. A. V. Belitsky and G. P. Korchemsky, “Exact null octagon,”1907.13131.

8. A. V. Belitsky and G. P. Korchemsky, “Octagon at finite coupling,”2003.01121. (click to hide)

Wed

06.05.

10:45

zoom: 301-229-497

Jan Manschot (Trinity College Dublin)

“Topological correlators in supersymmetric gauge theory”

abstract (click to view)
I will discuss topological correlators in 4d, N=2 supersymmetric gauge theory with gauge group SU(2). On an Euclidean, compact space-time, the contribution of the Coulomb branch to these correlators reduces to an integral over the effective coupling constant. Motivated by the decoupling of BRST exact observables, I will put forward a new prescription for the regularization and evaluation of these correlators. Joint work with G. Korpas, G. Moore, and I. Nidaiiev. (click to hide)

Wed

13.05.

16:00

zoom: 301-229-497

Aldo Riello (Perimeter Institute)

“The quasi-local degrees of freedom of Yang-Mills theory”

abstract (click to view)
Gauge theories possess nonlocal features that, in the presence of boundaries, inevitably lead to subtleties. In particular their fundamental degrees of freedom are not point-like. This leads to a non-trivial cutting (C) and sewing (S) problem: (C) Which gauge invariant degrees of freedom are associated to a region with boundaries? (S) Do the gauge invariant degrees of freedom in two complementary regions R and R’ unambiguously comprise *all* the gauge-invariant degrees of freedom in M = R ∪ R’ ? Or, do new “boundary degrees of freedom” need to be introduced at the interface S = R ∩ R’ ? In this talk, I will address and answer these questions in the context of Yang-Mills theory. The analysis is carried out at the level of the symplectic structure of the theory, i.e. for linear perturbations over arbitrary backgrounds. I will also discuss how the ensuing results hint towards a quasilocal derivation of the superselection of the electric flux through the boundary of a region, and into a novel gluing formula which constructively proves that no ambiguity exists in the gluing of regional gauge-fixed configurations. Time allowing I will also address how the formalism generalizes the “Dirac dressing” of charged matter fields, and how, in the presence of matter, quasi-local “global” charges (as opposed to gauge charges) emerge at symmetric (i.e. reducible) configurations.

This talk is based on arXiv:1910.04222, with H. Gomes (U. of Cambridge, UK).

See also arXiv:1808.02074, with H. Gomes and F. Hopfmüller (Perimeter) (click to hide)

This talk is based on arXiv:1910.04222, with H. Gomes (U. of Cambridge, UK).

See also arXiv:1808.02074, with H. Gomes and F. Hopfmüller (Perimeter) (click to hide)

Wed

20.05.

10:45

zoom: 301-229-497

Alba Grassi (CERN)

“Extremal correlators and Random Matrix Theory”

Wed

27.05.

10:45

zoom: 301-229-497

Andrea Puhm (Ecole Polytechnique)

“Infrared aspects of gravity and flat space holography”

abstract (click to view)
The realization that soft theorems in gauge theory and gravity are manifestations of Ward identities for asymptotic symmetries has reinvigorated recent attempts at flat space holography. One of the key milestones from applying this paradigm is that it solidifies a conjectured extension of the BMS group to include superrotations, based on a newly discovered subleading soft graviton theorem. This precipitated two parallel initiatives within the field. On the one hand, the subleading soft graviton mode is a natural stress tensor candidate for a putative dual celestial CFT with a Virasoro symmetry, which provoked reexamining scattering amplitudes in a basis that makes conformal covariance manifest. On the other hand, the correspondence between the subleading soft graviton theorem and the proposed asymptotic Virasoro superrotation symmetry does not appear to be bijective and an extension to arbitray diffeomorphisms on the celestial sphere was suggested. In this talk I will provide a unified treatment of conformally soft Goldstone modes of spontaneously broken asymptotic symmetries which will land us at the crossroads of the two ongoing debates about what the appropriate conformal basis for celestial CFT is and what the asymptotic symmetry group of Einstein gravity at null infinity should be. (click to hide)

Wed

03.06.

10:45

zoom: 301-229-497

Stefan Hohenegger (Université de Lyon)

“Symmetries in A-Type Little String Theories”

abstract (click to view)
In this talk, I discuss Little String Theories (LSTs), which are a type of interacting quantum theories whose UV-completion contains string-like (i.e. extended) degrees of freedom without gravitation. I focus on the so-called A-type LSTs, which can be described in M-theory through N parallel M5-branes arrayed on a circle or through F-theory compactified on a toric Calabi-Yau threefold. I argue that these LSTs allow for various dual low energy limits, describing quiver gauge theories with different gauge- and matter content. These dualities in turn imply a dihedral symmetry for any individual such theory, which acts intrinsically non-perturbative from the gauge theory perspective. Exploiting this symmetry I provide evidence for numerous interesting structures of the free energy, notably a decomposition of the leading instanton order, which is reminiscent of (effective) Feynman diagrams. The effective coupling functions appearing in this fashion show certain similarities with so-called modular graph functions, which have appeared in the study of Feynman amplitudes in string- and field theory. (click to hide)

last modified: Mon, 25 May 2020, 10:33 CEST