Abstract
We derive the ground state thermodynamic Bethe ansatz equations for the quantum deformation of the AdS5 × S5 mirror model, taking the deformation parameter to be a root of unity. By virtue of the deformation, the resulting equations show an interesting structure between a finite number of Y-functions.
Highlights
Integrability has and continues to play an important role in the context of the AdS/CFT correspondence [1], where it might provide us with the first opportunity ever to exactly solve an interacting field theory at the quantum level
Major achievements have been made in the spectral problem of N = 4 SYM in the planar limit [2] by its equivalence to a two dimensional integrable quantum field theory; the world-sheet theory of the AdS5 × S5 superstring in the light-cone gauge [3]
These developments conceptually culminated in the formulation of the thermodynamic Bethe ansatz equations [4,5,6] describing the spectrum of the world-sheet theory at finite size and finite coupling through the thermodynamics of an accompanying mirror model [7, 8]
Summary
Integrability has and continues to play an important role in the context of the AdS/CFT correspondence [1], where it might provide us with the first opportunity ever to exactly solve an interacting field theory at the quantum level. The prototypical example of a q-deformed model, the XXZ spin chain, shows a very interesting structure in its TBA equations when q is a root of unity [17, 18]; there are only finitely many Y-functions, some coupling in a non-standard fashion With this in mind, in the present paper we will derive the TBA equations for the quantum deformed theory at q. As we will show in this paper, when we analogously couple the two psuq(2|2) systems the spectrum of momentum carrying particles of the deformed mirror theory naturally terminates at bound states of length k These bound states and their scattering properties arrange themselves perfectly with the subsystems, resulting in the TBA structure illustrated in figure 4. Technical details regarding the S-matrix (including its pseudo-unitarity), string hypothesis, TBA kernels, the simplified TBA equation for Yk, and representation theory of psuq(2|2) have been collected in five appendices
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