Integrable spin chains in twisted maximally supersymmetric Yang-Mills theory

TL;DR

This paper identifies an integrable spin-chain description for an angular dipole deformation of N=4 SYM, which preserves classical scale invariance. Planar two-point functions in the invariant (0,1) plane map to a diagonally twisted SYM spin chain whose bulk interactions match the undeformed theory, with the twist encoded in boundary conditions; the dual string theory is a TsT-deformed AdS5×S5 background, and the asymptotic spectra agree via twisted Bethe Ansatz and standard integrability tools. Outside the invariant plane, conformal symmetry is broken, but a formal spin-chain interpretation can be obtained by translating operators to the invariant plane using Wilson lines, suggesting integrability extends to a broader twisted landscape. Overall, the work provides a concrete, nontrivial test of AdS/CFT for twisted integrable deformations and outlines a path toward a more general framework for Yang-Baxter deformations in holography.

Abstract

We study an angular dipole deformation of maximally supersymmetric Yang-Mills theory (SYM) that preserves its classical scale invariance. We show that two-point functions of suitable single trace operators, restricted to an invariant plane, are determined by scaling dimensions computable from an integrable spin chain. This spin chain is a diagonally twisted version of the famous integrable spin chain of SYM. It matches expectations from the dual string theory perfectly, presenting a precision test of holography in this new setting, and an important step to understanding general twisted integrable AdS/CFT.

Figures (2)

• Figure 1: Planar tree level contractions between two operators with six fields. Planarity allows only the canonical contraction (pictured on the left), plus cyclic shifts thereof. Each gives the same result, up to a phase, resulting in a split into twisted sectors, reflected by the sum above and in eqn. \ref{['eq:twistedsectorsplit']}.
• Figure 2: A planar four point interaction between two operators with three fields. Star products act from left to right on subsequent lines. We removed the middle star product on the interaction term by the planar equivalance theorem. By associativity we isolate star products acting on the lines contracted with the interaction term, canceling them by Lorentz invariance of the propagators. The remaining star products cancel because the undeformed contraction via the interaction term is Lorentz invariant, like the remaining propagator.