The TTbar deformation of two dimensional QFTs has various attractive and interesting features, giving a simple CDD deformation of the S matrix, and for instance preserving integrability, if present. As a simple example, deforming massless free scalars gives a Nambu-Goto string in flat space in a uniform light-cone gauge. I will discuss what happens if we deform "twice", i.e. TTbar deform light-cone gauge fixed string sigma models. In this setting, TTbar deformations can be viewed as TsT transformations in a suitable T dual frame. This TsT picture also gives a natural interpretation of the TTbar CDD factor as a Drinfeld-Reshetikhin twist.

The appearance of integrability in the duality between the AdS5xS5 string and planar maximally supersymmetric Yang-Mills theory gives rise to many insightful results. Various deformations of this AdS/CFT dual pair are known to also be integrable, prompting the question how far the power of integrability extends in this setting. In recent years there has been a lot of progress in answering this question. Rather than trying to demonstrate integrability in known AdS/CFT dual pairs, efforts instead focused on finding manifestly integrability preserving deformations of the AdS5xS5 string. While constructed to preserve integrability, the resulting so-called Yang-Baxter sigma models are, however, not guaranteed to describe strings, or have an AdS/CFT interpretation. The former of these points has since been addressed and turns out to be closely related to (nonabelian) T duality, and we now understand which of these models continue to describe strings. The goal of my talk is to address the latter point, regarding the AdS/CFT interpretation of these models. I will use symmetry considerations to give a unified AdS/CFT picture for these Yang-Baxter strings as duals to various noncommutative deformations of supersymmetric Yang-Mills theory. My general conjecture matches many known dualities, and I will briefly discuss nontrivial tests in various new cases, in the form of brane constructions indicating the desired dualities.

In the setting of integrability in AdS/CFT, in the typical approach to the AdS_5 x S^5 string a light-cone gauge is fixed, breaking Lorentz invariance on the worldsheet. One attempt to avoid the need for this goes under the name of Pohlmeyer reduction. Recently an S-matrix was conjectured to describe the scattering of solitons in this theory. Now as I will explain in my talk, the S-matrix of an integrable quantum field theory together with its dispersion relation are enough to find its finite volume spectrum exactly, through the so-called thermodynamic Bethe ansatz. I will work this out for an S-matrix and dispersion that interpolate between the standard light-cone gauge fixed superstring and this conjectured Pohlmeyer S-matrix, by analogy to a simpler model. Viewed as a deformation of the light-cone gauge fixed superstring TBA, this story is very similar to deforming the XXX spin chain to the XXZ one, which I will concretely discuss. I will finish by emphasizing important differences to this simple toy model, and discuss surprises in the so-called Y-system associated to the TBA equations.