TALKS

Integrability underlies the AdS3/CFT2 correspondence in presence of Ramond-Ramond (RR) and Neveu-Schwarz-Neveu-Schwarz (NSNS) fluxes. For the special case of backgrounds with NSNS fluxes only, the integrable structure simplifies drastically and appears to be closely related to a TTbar deformation of a free theory. I will sketch how this integrability construction allows us to reproduce the Wess-Zumino-Witten spectrum exactly, and how it may be generalised to correlation functions.

In this talk, I will consider integrable quantum field theories deformed by some kind of CDD factors. The models involve just one kind of stable particle.  These deformations are related with the TTbar and generalized TTbar deformations.   These models have a factorizable S-matrices and their ground state energies E(R) with the spatial  coordinate compactified on a circle  of circumference R can be computed by the Thermodynamic Bethe Ansatz (TBA) equations. I will show that the TBA equations for various models exhibit two real solutions (the primary and secondary branches)  at R greater than a certain critical parameter-dependent value R* (a square-root branching point).  This behavior of E(R) is qualitatively the same as the one for standard TTbar deformations of  local QFT. The singularity signals a Hagedorn behavior of the density of high energy states.  I will finish the talk mentioning several open questions.

The ODE / IM correspondence is a remarkable link between classical integrable models, Bethe Ansatz and nonlinear integral equations for finite volume integrable Quantum Field Theories. Within the sin(h)-Gordon framework, I will show that the ODE/IM  remains valid also after classical/quantum TTbar deformation.

Various holographic set-ups in string theory suggest the existence of non-local, UV complete two- dimensional QFTs that possess a Virasoro symmetry,  in spite of their non- locality. I will argue that JTbar- deformed CFTs are the first concrete realisation of such a QFT,  through a detailed analysis of their classical and quantum symmetry algebra.

A class of noncritical AdS$_3$ backgrounds with NS fluxes have CFT duals given by a deformed symmetric product, whose properties can be derived by a systematic investigation of the worldsheet description.  The extension of the CFT to a linear dilaton regime, related to the TTbar deformation, is briefly described.

Abstract: Since holographic duality had been conjectured, it has been immediately suggested that dynamics along the emergent extra-dimensional space describes a renormalization group (RG) flow of the corresponding quantum field theory (QFT). Following this idea, we develop an emergent holographic description of a QFT, where not only the information of the RG flow is introduced into an IR holographic dual effective field theory (HDEFT), but also the UV information of the QFT is specified into the HDEFT through the IR boundary condition. In particular, we argue that this dual holographic construction is self-consistent at least even if not exact, showing two aspects: The solution of the Hamilton-Jacobi equation is given by the IR boundary effective action, and the Ward identity is satisfied naturally. We discuss the role of the RG β−function in the bulk effective dynamics of the metric tensor near a conformally invariant fixed point. We claim that this emergent dual gravity theory generalizes the AdSD+1−CFTD duality conjecture away from quantum criticality.​

We describe the symmetries of Witten’s cigar, emphasizing its similarity to Liouville theory. In particular, we introduce the S-matrix of the model as an operator with conformal and W-symmetry. We then discuss the TTbar deformation of these structures.

In this talk, I will present some new results on the TTbar and more general solvable irrelevant deformations of quantum field theories with integrable boundaries and defects. I will first discuss the deformed boundary and defect scattering matrices and then consider the deformation of other important physical quantities such as the spectrum and the exact g-function.

I discuss the features of certain integrable spin chains one obtains from the dilatation operator of strongly twisted, double-scaled deformations of N = 4 Super Yang-Mills Theory. A particular case is a certain chiral three-state model with an exceedingly simple Hamiltonian. It is non-diagonalizable, and shows very rich and intricate patterns of Jordan cell formation. I explain some of the difficulties one faces when applying the quantum inverse scattering method to these models. I also sketch how to find a beautiful solution to this problem. Finally, I will briefly discuss some relations to logarithmic four-dimensional quantum field theories and in particular the resulting challenges for a complete understanding of fishnet-type models.

The discovery of integrability in planar N=4 sYM theory led to considerable advances in the computation of planar anomalous dimensions. In this talk I will discuss universal statistical properties of anomalous-dimension spectra in sYM theories in the planar limit and at finite rank of the gauge group. I will show how they can give insight into the nature of the underlying model, in particular we will see integrability manifest itself in spectra of integrable spin chains, while non-planar spectra, as well as spectra of non-integrable spin chains, can be described by random matrix theory.

TBA

Integrability in the spectral problem of the planar N=4 SYM and its cousins enabled us to determine exact conformal anomalous dimensions. During the last 20 years, the conjectured quantum integrability was checked perturbatively at various 't Hooft coupling regimes. Nevertheless, a complete proof of the integrability is not yet successful. On the other hand, there has been a general belief that integrability will be broken in a generic non-planar situation, but quantitative confirmation has just been made last year. Namely, the transition from integrability to chaos was observed by studying the level statistics in both planar and non-planar spectrum. In our work, we study the out-of-time ordered correlators(OTOCs) in non-planar SYM and find the appearance of quantum chaos. Our work provides a nontrivial check for the chaotic nature of generic non-planar situations in SYM.

In this talk we consider the most general (beyond TTbar) deformation of the  2D O(N+1) σ-model by the irrelevant dimension-four operators.  The theory deformed in this way is generally not integrable, and its S-matrix loses the factorization properties.  We present an overview of the method of exact all-order summation of leading infrared  logarithms in 2D massless φ4-type non-renormalizable effective field theories (EFTs).  It is based on the fundamental requirements of unitarity, analyticity and crossing symmetry of scattering amplitudes and generalizes the renormalization group technique for the case of non-renormalizable EFTs.   This method allows us to provide the exact results for the  2 → 2 S-matrix in the leading logarithmic  approximation in the deformed 2D O(N+1) σ-model. In particular, we present the remarkable solution  expressed in terms of elliptic functions leading to scattering amplitudes with a doubly periodic structure of the Landau  poles. We discuss the new insights into the properties of the theories deformed by irrelevant operators more general than  the TTbar deformation from the perspective of our approach.TBA

In this talk, I discuss TTbar deformations of d=2 theories with fermions with a view toward the quantization. First I discuss the canonical analysis of TTbar deformation of free scalar field and free fermion. Then I explain how the canonical analysis can reproduce the well-known deformed spectrum perturbatively. I also consider the (non-SUSY) TTbar deformation of free N=(1,1) SUSY model. Based on the canonical analysis, I will show that the deformed model preserve supersymmetry in all order by constructing the supercharge explicitly. I also discuss the relation ot 3D N=2 Green-Schwarz superstring action.  I will explain how broken) N=2 3D spacetime SUSY is identical to TTbar deformed N=(1,1) SUSY together with fermi global charges.

TBA

TBA

Pure TTbar deformations of conformal field theories are generally asymptotically incomplete in the ultra-violet (UV) due to square-root singularities in the ground state energy on a cylinder of circumference R, such that the theory is ill-defined for distances shorter than some critical R*. In this article we show how a theory can be completed if one includes an infinite number of additional irrelevant perturbations. This is fully demonstrated in the case of the Ising model at cIR= 1/2 in the infra-red (IR), where we find two completions with central charges cUV = 3/2 and cUV = 7/10, the latter being the tri-critical Ising model. Both of these UV completions have N=1 supersymmetry which is broken in the renormalization group flow to low energies. We also consider multiple TTbar deformations of a free massless boson, where we cannot find a UV completion that is consistent with the c-theorem. For negative coupling g, which violates the c-theorem, in both cases we find cUV = - cIR as g → - ∞. Finally we also study pure TTbar deformations of the off-critical Ising model.

We comment on the similarities and differences between TTbar-deformed relativistic and non-relativistic models, and use one-soliton solutions of the deformed NLS and KdV models to discuss the phenomenon of widening/narrowing width of particles under the TTbar deformation.