Strong coupling expansion of Baxter equation in N=4 SYM

TL;DR

This work addresses the problem of computing all-order anomalous dimensions in $ ext{N}=4$ SYM by a deformed noncompact $ ext{sl}(2)$ Baxter equation and develops a systematic strong-coupling, single-logarithmic expansion in the regime of large conformal spin. By reformulating the spectrum in terms of Riemann-Hilbert problems for Bethe-root resolvents and expanding in inverse coupling $1/g$, the authors derive explicit leading and subleading results. They construct the leading two-cut (genus-one) solution, obtain the resolvents $G_0$ and $G_1$, and compute the local integrals of motion $ olinebreak \\mathcal{Q}_r(g)$ to order $g^{-1}$, reproducing the cusp anomalous dimension for $r=2$ as a consistency check. This provides analytical control over the strong-coupling behavior of all-order anomalous dimensions in the $ ext{sl}(2)$ sector and establishes a framework for systematic higher-order corrections.

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.