Integrable twists in AdS/CFT

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.

v2: references and clarifications added, 46 pages

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• Is Vtb=1 ?
• Integrability of classical strings dual for noncommutative gauge theories
• Reflecting magnons
• Multispin Giant Magnons
• Integrability of the AdS_5 x S^5 superstring and its deformations
• Review of AdS/CFT Integrability, Chapter IV.2: Deformations, Orbifolds and Open Boundaries
• The spectral problem for strings on twisted AdS_5 x S^5
• A new coordinate system for q-deformed AdS_5 x S^5 and classical string solutions
• Quantum integrability and functional equations
• Integrable deformations of the AdS${}_5\times$S${}^5$ superstring and the classical Yang-Baxter equation -- Towards the gravity/CYBE correspondence --
• Spiky Strings, Giant Magnons and beta-deformations
• Finite-Size Effects for Multi-Magnon States
• On the perturbative chiral ring for marginally deformed N=4 SYM theories
• Notes on beta-deformations of the pure spinor superstring in AdS(5) x S(5)
• On the anatomy of multi-spin magnon and single spike string solutions
• The Leigh-Strassler Deformation and the Quest for Integrability
• Melvin Twists of global AdS_5 \times S_5 and their Non-Commutative Field Theory Dual
• Spin Chain with Magnetic Field and Spinning String in Magnetic Field Background
• A note on the universality of the Hagedorn behavior of pp-wave strings
• Three Spin Spiky Strings in beta-deformed Background
• Jordanian spin chains for twisted strings in $Ad{S}_5\times S^5$
• Comments on the slope function