Strong coupling expansion of Baxter equation in N=4 SYM

TL;DR

This paper develops a strong coupling expansion of the Baxter equation in N=4 SYM, providing a systematic method to analyze anomalous dimensions and conserved charges in the theory.

Contribution

It introduces a systematic strong coupling expansion of the Baxter equation in the single-logarithmic limit, overcoming previous asymptotic limitations.

Findings

Explicit construction of resolvents at lowest two orders in strong coupling

Derivation of local conserved charges of the spin chain

Reduction to Riemann-Hilbert problems for Bethe root resolvents

Abstract

The anomalous dimensions of single-trace local Wilson operators with covariant derivatives in maximally supersymmetric gauge theory are believed to be generated from a deformed noncompact sl(2) Baxter equation. We perform a systematic expansion of this equation at strong coupling in the single-logarithmic limit of large conformal spin to overcome the limitation of the asymptotic nature of the equation. The analysis is reduced to Riemann-Hilbert problems for corresponding resolvents of Bethe roots in each order of the quasiclassical expansion. We explicitly construct the resolvents in the lowest two orders in strong coupling and find all local conserved charges of the underlying long-range spin chain.