q-deformation of the AdS5 × S5 superstring S-matrix and its relativistic limit

Abstract

A set of four factorizable non-relativistic S-matrices for a multiplet of fundamental particles are defined based on the R-matrix of the quantum group deformation of the centrally extended superalgebra su(2|2). The S-matrices are a function of two independent couplings g and q = e iπ/k . The main result is to find the scalar factor, or dressing phase, which ensures that the unitarity and crossing equations are satisfied. For generic (g, k), the S-matrices are branched functions on a product of rapidity tori. In the limit k → ∞, one of them is identified with the S-matrix describing the magnon excitations on the string world sheet in AdS 5 × S 5 , while another is the mirror S-matrix that is needed for the TBA. In the g → ∞ limit, the rapidity torus degenerates, the branch points disappear and the S-matrices become meromorphic functions, as required by relativistic S-matrix theory. However, it is only the mirror S-matrix which satisfies the correct relativistic crossing equation. The mirror S-matrix in the relativistic limit is then closely related to that of the semi-symmetric space sine-Gordon theory obtained from the string theory by the Pohlmeyer reduction, but has anti-symmetric rather than symmetric bound states. The interpolating S-matrix realizes at the quantum level the fact that at the classical level the two theories correspond to different limits of a one-parameter family of symplectic structures of the same integrable system. arXiv:1112.4485v1 [hep-th]

Massive S-matrix of AdS3×S3×T4 superstring theory with mixed 3

“…It would be interesting also to construct an exact 3-parameter (h, q, k) S-matrix that interpolates (as in the AdS 5 × S 5 case [35]) between the exact superstring S-matrix parametrized by (h, q) and the exact relativistic S-matrix of the corresponding Pohlmeyer-reduced theory [1,4,36] parametrized by (q, k). 21 As was shown in [1], the Pohlmeyer-reduced theory in the q = 0 case depends on q only through the mass scaleμ =qµ, i.e.…”

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

“…It appears that this centrally extended psu(2|2), or more precisely its universal enveloping algebra, admits a natural deformation psu q (2|2) in the sense of quantum groups [6,7]. This algebraic structure is the starting point for the construction of a psu q (2|2) ⊕ psu q (2|2)-invariant S-matrix, giving a quantum deformation of the AdS 5 × S 5 world-sheet S-matrix [6,8,9]. The deformation parameter q can be an arbitrary complex number, but in physical applications is typically taken to be either real or a root of unity.…”

“…The aim of the present work is to compute the 2 → 2 scattering matrix for the η-deformed model in the limit of large string tension g and to compare the corresponding result with the known q-deformed S-matrix found from quantum group symmetries, unitarity and crossing [6,8]. In the context of the undeformed model a computation of this type has been carried out in [22].…”

“…The gauge dependent terms multiplying (2a − 1) are invariant under SO (8) as in the underformed case.…”

Anisotropic Landau-Lifshitz sigma models from q-deformed AdS5×S5 superstrings

“…There are two approaches to tackle this issue. The one is an algebraic approach based on q-deformations of the worldsheet S-matrix [12][13][14][15][16][17][18][19]. The deformed S-matrices are constructed in a mathematically consistent way.…”