The $AdS_5$x$S^5$ string spectrum, Pohlmeyer reduction and quantum deformations
Stijn van Tongeren
Fri, Nov. 16th 2012, 14:15
Salle Claude Itzykson, Bât. 774, Orme des Merisiers
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.