Talks

Each day will have a morning session from 10:30-12:20 and an afternoon session from 14:10-16:00. A provisional programme of speakers for each session is as follows:

Monday

Morning

Speakers: Charlotte Kristjansen/Georgios Linardopoulos
Title: Scalar one-point functions and matrix product states of AdS/dCFT
Slides (Kristjansen)
Slides (Linardopoulos)
Abstract: We present in a closed form all scalar one-point functions of the defect CFT dual to the D3-D5 probe brane system with k units of flux which are calculated as the overlap between a Bethe eigenstate of the integrable SO(6) spin chain and a certain matrix product state of bond dimension k. This matrix product state is shown to be annihilated by all the parity odd charges of the spin chain which has recently been suggested as the criterion for such a state to correspond to an integrable initial state. We discuss the properties of the analogous matrix product state for the SO(5) symmetric D3-D7 probe brane set-up and summarize the status of the calculation of one-point functions in the D3-D7 case.

Afternoon

Speaker: Balázs Pozsgay
Title: Integrable states in spin chains and exact overlap formulas
Slides
Abstract: Motivated by the study of quantum quenches in spin chains we introduce a definition of "integrable initial states". We review special properties of these states in the spin-1/2 XXZ chain, and we argue that in this case all integrable initial states can be obtained by the boundary Algebraic Bethe Ansatz (b-ABA). We present exact overlap formulas for them, including states created by the so-called off-diagonal K-matrices. We also discuss higher rank spin chains, where certain MPS have been constructed that are relevant for one-point functions in AdS/CFT. They have recently been proven to be integrable by other authors. All cases are unified by the similar structure for the overlaps, which involves so-called Gaudin-like determinants. The interpretation of the higher rank cases within b-ABA is an open problem, that will be discussed too.

Tuesday

Morning

Speaker: Nikolay Gromov
Title: Structure constants and QSC
Slides
Abstract: We give a pedagogical introduction to the Quantum Spectral Curve of N=4 SYM and discuss its applications to correlation functions. We find a massive simplification in the non-perturbative expression for the structure constant of Wilson lines with 3 cusps when expressed in terms of the key Quantum Spectral Curve quantities, namely Q-functions. Our calculation is done for the configuration of 3 cusps lying in the same plane with arbitrary angles in the ladders limit. This provides strong evidence that the Quantum Spectral Curve is not only a highly efficient tool for finding the anomalous dimensions but also encodes correlation functions with all wrapping corrections taken into account to all orders in the `t Hooft coupling. We also show how to study the insertions of scalars coupled to the Wilson lines and extend our result for the spectrum and the structure constant for these states. We discuss an OPE expansion of two cusps in terms of these states. Our results give additional support to the Separation of Variables strategy in solving the planar N = 4 SYM theory.

Afternoon

Speaker: Benjamin Basso/Deliang Zhong
Title: Fishnet session
Slides (Deliang)

Wednesday

Morning

Speaker: Paul Heslop
Title: Quantum Gravity from Conformal Field Theory
Slides
Abstract: AdS/CFT relates certain correlation functions in N=4 SYM to supergravity amplitudes in AdS space. In this talk I give an outline of recent progress in which we use this duality together with CFT bootstrap techniques to obtain one loop quantum gravity amplitudes. Along the way we need to resolve a large N degeneracy of double trace operators and as a byproduct of our investigations obtain the leading corrections to the anomalous dimensions of all double trace operators of supergravity bound states. I will also briefly discuss M theory corrections and data for the M5 brane world volume theory.

Afternoon

Speaker: Xinan Zhou
Title: Holographic Mellin Amplitudes in Various Dimensions
Slides
Abstract: Holographic four-point functions are known for their notorious computational difficulties. In the past two decades, only a handful of them have been explicitly calculated using the standard algorithm. In this talk I will introduce modern methods to compute holographic correlators efficiently, which are inspired by the bootstrap philosophy and the on-shell methods of scattering amplitudes in flat space. I will show that by translating the problem into Mellin space many difficulties encountered when applying the traditional method are avoided. I will argue that imposing symmetry constraints and general consistency conditions -- avoiding all details of the complicated effective Lagrangian -- leads to many novel results for holographic four-point functions in AdS5×S5, AdS7×S4, AdS4×S7 and AdS_6×_w HS4. I will conclude by outlining some interesting future directions of this program.

Thursday

Morning

Speaker: Zoltan Bajnok
Title: Form factors in finite volume.
Slides
Abstract: We initiate a systematic method to calculate both the finite volume energy levels and form factors from the momentum space finite volume two-point function. By expanding the two point function in the volume we extracted the leading exponential volume correction both to the energy of a moving particle state and to the simplest non-diagonal form factor. The form factor corrections are given in terms of a regularized infinite volume 3-particle form factor and terms related to the L\"usher correction of the momentum quantization. We tested these results against second order Lagrangian and Hamiltonian perturbation theory in the sinh-Gordon theory and we obtained perfect agreement.

Afternoon

Speaker: Ivan Kostov
Title: TBA and tree expansion
Slides
Abstract: We present a derivation of the partition function of the thermal ensemble of an integrable theory with diagonal scattering by evaluating the trace of the evolution operator over the Hilbert space. The derivation is based on the expansion of the Gaudin determinant as a sum of spanning trees.

Friday

Morning

Speaker: Yunfeng Jiang/Burkhard Eden
Title: Colorful hexagons and non-planar integrability
Abstract: This is a combined talk given by Burkhard Eden (BE) and Yunfeng Jiang (YJ). In the first part of the talk, YJ will review the hexagon tessellation approach to four-point functions. Then he will focus on the four-point functions with two non-BPS operators where one can see the necessity of taking into account color factors. Finally he will show that the color factors are also important for loop level four-point functions as well as torus two-point functions. In the second part of the talk, BE will discuss how to compute correlation functions involving double-trace operators, as well as more general 1/N effects; in particular he will discuss in detail the whole next-to-leading order in the large-N expansion of tree-level BMN two-point functions by tessellating a torus with punctures.

Afternoon

Speaker: João Caetano/Till Bargheer
Title: Integrability for Non-planar N=4 SYM
Slides(Bargheer)