Integrable twists in AdS/CFT

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 S5 target subspace in the holographic dual on AdS5 x S5. We present here an analogous set of deformations that act on global toroidal isometries in the AdS5 subspace. Remarkably, certain sectors of the string theory remain classically integrable in this larger class of so-called γ-deformed AdS5 x S5 backgrounds. Relying on studies of deformed su(2)γ models, we formulate a local sl(2)γ 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 AdS5 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)γ and su(2)γ 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 β-deformed gauge theory