The quantum deformed mirror TBA II

Abstract

Abstract:We discuss the description of generic excited states in the quantum deformed AdS 5 × S 5 mirror thermodynamic Bethe ansatz and derive the associated Y-system. This Y-system shows an interesting new feature; it depends explicitly on the excited state under consideration. Similarly, it also depends on twisted boundary conditions. We construct the asymptotic solution of these TBA and Y-system equations by deriving the twisted transfer matrix for the quantum deformed Hubbard model and finding the deformed mirror bound state dressing phase. This asymptotic construction is insensitive to the precise nature of the deformation, and thereby provides a nontrivial check of the interesting new features which arise precisely at roots of unity.

S-matrix for strings on η-deformed AdS5 × S5

“…While this program has been successfully carried out for deformations with q being a root of unity [11,12], the corresponding string background remains unknown. There is a conjecture that in the limit of infinite 't Hooft coupling the q-deformed S-matrix tends to that of the Pohlmeyer-reduced version of the AdS 5 × S 5 superstring [13,14].…”

“…The S-matrix compatible with psu(2|2) q symmetry [6] has been studied in detail in the recent papers [8,11,12,14]. To make the present paper self-contained, in this appendix we recall its explicit form following the same notation as in [11].…”

Integrability of the ${\rm Ad}{{{\rm S}}_{5}}\times {{{\rm S}}^{5}}$ superstring and its deformations

“…30 The derivation of the eigenvalues of these transfer matrices is of course a close variation on the undeformed derivation. Before stating the result, let us introduce the following shorthand notation 28 For more details see [221,222]. 29 The alternative characterization in terms of the large M limit of the Y M |(v)w functions we saw before does not apply here of course.…”

Pulsating strings on (AdS3 × S3) ϰ

“…The other way is an algebraic approach based on q-deformations of the world sheet S-matrix [16][17][18][19][20][21][22][23]. Recently one real deformed parametered integrable qdeformed AdS 5 × S 5 super coset model with fermionic degree of freedom was found in [24].…”