An integrable deformation of the AdS_5 x S^5 superstring action

TL;DR

This work constructs a systematic integrable deformation of the type IIB AdS5×S5 superstring by introducing a skew-symmetric $R$-matrix solving the modified classical Yang–Baxter equation and a deformation parameter $\eta$. The deformed action $S[g]$ is explicitly defined via the invertible operator $1-\eta R_g\circ d$, and its integrability is established through a Lax pair with spectral parameter, along with preserved gauge and kappa-symmetries, and Virasoro constraints. In the $\eta\to0$ limit, the model reproduces the Metsaev–Tseytlin action; the deformation is expected to q-deform the underlying psu(2,2|4) symmetry, linking to q-deformed S-matrices and Pohlmeyer-reduced theories. The results provide a concrete framework for exploring integrable deformations of AdS5×S5 with potential insights for holography and quantum groups.

Abstract

An integrable deformation of the type IIB AdS_5 x S^5 superstring action is presented. The deformed field equations, Lax connection, and kappa-symmetry transformations are given. The original psu(2,2|4) symmetry is expected to become q-deformed.