Integrable twists in AdS/CFT

TL;DR

This paper explores integrable deformations of the AdS_5 x S^5 background in string theory, extending known marginal deformations to include gamma-deformations that preserve classical integrability and allow for spectral analysis via Bethe equations.

Contribution

It introduces a new class of gamma-deformed AdS_5 x S^5 backgrounds with preserved integrability and formulates corresponding Bethe equations for spectral analysis.

Findings

Certain sectors remain classically integrable after deformation

Derived Bethe equations encode the spectrum of deformed backgrounds

Validated the approach with near-pp-wave energy spectra

Abstract

A class of marginal deformations of four-dimensional N=4 super Yang-Mills theory has been found to correspond to a set of smooth, multiparameter deformations of the S^5 target subspace in the holographic dual on AdS_5 x S^5. We present here an analogous set of deformations that act on global toroidal isometries in the AdS_5 subspace. Remarkably, certain sectors of the string theory remain classically integrable in this larger class of so-called gamma-deformed AdS_5 x S^5 backgrounds. Relying on studies of deformed su(2)_gamma models, we formulate a local sl(2)_gamma Lax representation that admits a classical, thermodynamic Bethe equation (based on the Riemann-Hilbert interpretation of Bethe's ansatz) encoding the spectrum in the deformed AdS_5 geometry. This result is extended to a set of discretized, asymptotic Bethe equations for the twisted string theory. Near-pp-wave energy spectra within sl(2)_gamma and su(2)_gamma sectors provide a useful and stringent test of such equations, demonstrating the reliability of this technology in a wider class of string backgrounds. In addition, we study a twisted Hubbard model that yields certain predictions of the dual beta-deformed gauge theory.