1st Day

● Joao Caetano: Maximally Supersymmetric RG Flows in 4D and Integrability [Caetano.pdf]

In this talk, we revisit the leading irrelevant deformation of N=4 Super Yang-Mills theory that preserves sixteen supercharges. We consider the deformed theory on S3×R. We are able to write a closed form expression of the classical action thanks to a formalism that realizes eight supercharges off shell. We then investigate integrability of the spectral problem, by studying the spin-chain Hamiltonian in planar perturbation theory. We also comment on the holographic interpretation of the theory.

● Akikazu Hashimoto: Observables of TT-bar deformed CFTs and generalizations

For a CFT deformed simultaneously by TT-bar, JT-bar, and TJ-bar, I will describe two concrete physical observables. One is the torus partition function, and the other is the entanglement entropy. I will also discuss some applications.

In this talk I will show how a T-Tbar transformation on the worldsheet of a string non-linear sigma model can be interpreted as a TsT transformation of the target-space geometry.

Surprising synergies occur when research threads come to together. I will explain how AdS/CFT led to new insights on Yang-Baxter deformations, which in turn led to new O(d,d) transformations with non-constant entries. TTbar deformations in supergravity fall into the latter.

2nd Day

● Mark Mezei: TTbar-like theories and their symmetries [Mezei.pdf]

The solution of TTbar-deformed field theories opened a new window on the rich landscape of possible UV behaviors of quantum field theories. In this talk, we describe attempts and partial successes in probing this landscape further by studying close relatives of the TTbar deformation. The symmetries preserved by these special irrelevant deformations will play a pivotal role in the discussion.

● Song He:Correlation function in TTbar Deformed CFTs [He.pdf]

In this talk, we will focus on the recent progresses on construction of the correlation functions in TTbar deformed theories in perturbative way. Firstly, we will apply conformal Ward Identity and choose proper regulization procedure to obtain the first order deformation of the correlation function in various situations. To go beyond the second order deformation, one has to contain the TTbar flow effects and we explore a perturbative way to construct the correlation function, in particular, the second order deformation to the partition function in 2D free theories in terms of path integral formalism. 

● Roberto Tateo: A classical 4D generalisation of  the TTbar-deformation

Two-dimensional field theories deformed by Zamolodchikov's  TTbar operator have recently attracted the attention of theoretical physicists due to the many important links with string theory and AdS/CFT. In this talk, I will describe various classical and quantum aspects of this particular irrelevant perturbation, including  its  geometrical interpretation at the classical level. 

I will also introduce a  generalisation of this geometrical framework to 4D field theories, and discuss some of the interesting differences with the 2D case.

● Yunfeng Jiang: TTbar deformed 1d Bose gas [Jiang.pdf]

TTbar deformation was originally proposed as an irrelevant deformation for 2d relativistic quantum field theories. In this talk, I will show that the same kind of integrable deformation can be defined for a wide class of integrable models including quantum spin chains and continuous integrable many-body systems such as the Lieb-Liniger model. I will present the definition for the TTbar deformed 1d Bose gas and study its deformed spectrum and thermodynamics.

3rd Day

● Vladimir Rosenhaus: Integrability and renormalization under T barT

Smirnov and Zamolodchikov recently introduced a new class of two-dimensional quantum field theories, defined through a differential change of any existing theory by the determinant of the energy-momentum tensor. From this TT¯ flow equation one can find a simple expression for both the energy spectrum and the S-matrix of the TT¯ deformed theories. Our goal is to find the renormalized Lagrangian of the TT¯ deformed theories. In the context of the TT¯ deformation of an integrable theory, the deformed theory is also integrable and, correspondingly, the S-matrix factorizes into two-to-two S-matrices. One may thus hope to be able to extract the renormalized Lagrangian from the S-matrix. We do this explicitly for the TT¯ deformation of a free massive scalar, to second order in the deformation parameter. Once one has the renormalized Lagrangian one can, in principle, compute all other observables, such as correlation functions. We briefly discuss this, as well as the relation between the renormalized Lagrangian, the TT¯ flow equation, and the S-matrix.

● Mitsuhiro Nishida: Entanglement and Renyi Entropy of Multiple Intervals in TTbar Deformed CFT and Holography

We study the entanglement entropy (EE) and the Renyi entropy (RE) of multiple intervals in two-dimensional TTbar deformed conformal field theory (CFT) at finite temperature by field theoretic and holographic methods. First, by the replica method with the twist operators, we construct the general formula of the RE and EE up to the first order of a deformation parameter. By using our general formula, we show that the EE of multiple intervals for a holographic CFT is just a summation of the single interval case even with the small deformation. This is a non-trivial consequence from the field theory perspective, though it may be expected by the Ryu-Takayanagi formula in holography. However, the deformed RE of the two intervals is a summation of the single interval case only if the separations between the intervals are big enough. It can be understood by the tension of the cosmic branes dual to the RE. We also study the holographic EE for single and two intervals with an arbitrary cut-off radius (dual to the TTbar deformation) at any temperature. We confirm our holographic results agree with the field theory results with a small deformation and high temperature limit, as expected. For two intervals, there are two configurations for EE: disconnected (s-channel) and connected (t-channel) ones. We investigate the phase transition between them as we change parameters: as the deformation or temperature increases the phase transition is suppressed and the disconnected phase is more favored.

● Ioannis Papadimitriou: On AdS3 and AdS2 boundary conditions

I will present a systematic analysis of AdS3 and AdS2 boundary conditions and discuss their field theory interpretation.  

● Monica Guica: Infinite pseudo-conformal symmetries in TTbar, JTbar and JTa - deformed CFTs

TBA

4th Day

● Van Raamsdonk: Microscopic construction of Planck branes in AdS/CFT

In this talk, we describe BCFTs based on N=4 SYM theory on a half space which are dual to AdS5 x S5 with a dynamical end-of-the-world brane cutting off the UV region of the geometry for half of the space. We argue that gravity is approximately localized to this end-of-the-world brane, so it behaves as a Randall-Sundrum Planck brane. The gravity picture has similarities to the proposed gravity dual of T-Tbar deformations for holographic theories.

● Kyungkiu Kim: More on Phase Transition in deformed JT Gravity

In this paper we study a black hole phase transition noticed by Witten recently in a deformed JT gravity with an arbitrary potential. To investigate this transition, we take into account geodesic and a two-point function. In the case with locally negative potentials, the geodesic and the two-point function show signicantly different behavior from those in cases with a positive potential. This behavior can be interpreted as a contribution from a metastable excitation induced by the negative part of the potential. Also, we consider charged black holes and construct the corresponding phase diagram in terms of the metastable excitation. Also we study a map from this gravity model to CFT with a $Tbar{T}$ deformation.

● Jong-Hyun Baek: Holography of TTbar deformation in quantum mechanics

We discuss the holographic interpretation of T^2 deformation of quantum mechanical system. The deformation can be thought of as the dimensional reduction of TTbar deformation in 2d, which preserves the trace relation. 

The 2d dual gravity theory is Jackiw-Teitelboim gravity, which is a reduction of 3d Einstein gravity. The variation principle is employed to find the boundary conditions between deformed and undeformed theory. The mixed boundary conditions corresponds to Dirichlet boundary conditions at finite cutoff via on-shell condition. The trace of the deformed stress tensor in 2d gravity then reproduces the spectrum of the deformed quantum mechanical system such as Schwarzian theory.  We also comment on the JTbar deformation in 1d. 

● Shinji Hirano: Random Geometry Approach to TTbar Deformation [Hirano.pdf]

The objective of my talk is twofold: One is to develop further Cardy's random geometry approch to the TTbar deformation. In particular, it is applied to the computation of correlators of the TTbar deformed CFTs, including 4pt functions of the stress tensor. A few key results are the TTbar deformed Liouville theory and a somewhat surprising logarithmic correction to a 4pt stress tensor correlator. The other is to discuss the gravity dual of the TTbar deformed CFTs which becomes a straightforward application of AdS/CFT from the random geometry perspective. A remark will be made on the relation to the cutoff AdS interpretation. 

● Kentaroh Yoshida: TTbar-deformation and Liouville gravity

We consider a gravitational perturbation of the Jackiw-Teitelboim (JT) gravity with an arbitrary dilaton potential and study the condition under which the quadratic action can be seen as a TTbar-deformation of the matter action. As a special case, the flat-space JT gravity discussed by Dubovsky et al. [arXiv :1706 .06604] is included. Another interesting example is a hyperbolic dilaton potential. This case is equivalent to a classical Liouville gravity with a negative cosmological constant and then a TTbar-deformation of the matter action with a finite coupling is realized as a gravitational perturbation on AdS_2.

5th Day

● Jorrit Kruthoff: JT gravity at finite cutoff [Kruthoff.pdf]

We compute the partition function of 2D Jackiw-Teitelboim (JT) gravity at finite cutoff in two ways: (i) via an exact evaluation of the Wheeler-DeWitt wave-functional in radial quantization and (ii) through a direct computation of the Euclidean path integral. Both methods deal with Dirichlet boundary conditions for the metric and the dilaton. In the first approach, the radial wavefunctionals are found by reducing the constraint equations to two first order functional derivative equations that can be solved exactly, including factor ordering. In the second approach we perform the path integral exactly when summing over surfaces with disk topology, to all orders in perturbation theory in the cutoff. Both results precisely match the recently derived partition function in the Schwarzian theory deformed by an operator analogous to the TTbar deformation in 2D CFTs. This equality can be seen as concrete evidence for the proposed holographic interpretation of the TTbar deformation as the movement of the AdS boundary to a finite radial distance in the bulk.

● Yu Nakayama: Very special TJ deformations

TJ deformations of 2d CFT can be regarded as an analogue of one type of very special relativity studied by  Cohen and Glashow. Cohen and Glashow discussed how to add extra symmetry to study its phenomenological consequence (e.g. nutrino mass). I will study its analogue in d=2, given by a very special TJ deformation.

● Benjamin Doyon: TTbar deformations, the width of fundamental particles, and generalised hydrodynamics

I will explain how TTbar deformations of many-body systems - both relativistic and Galilean invariant - can be seen as deformations of the fundamental particles of the theory. In this interpretation, depending on the sign, either the particles gain a nonzero width - point particles become hard rods - or the space in-between them is made larger. This gives a simple explanation for the field-dependent change of coordinates that is known to reproduce TTbar deformations: it accounts for the reduced or enlarged free space. This also clarifies many aspects of TTbar deformations, such as their UV behaviours and scattering matrix. Field-dependent changes of metric, particle widths, and their relation to scattering have been explored, independently, in the context of generalised hydrodynamics, the hydrodynamic theory for integrable systems. I will review aspects of this, and explain some of the connections between the two areas of research.

Based on work in collaboration with John Cardy.

● Changrim Ahn: Exact S-matrix and RG flow for Super-Liouville Theory with (TTbar)_s deformations

TBA