On the strong coupling expansion in the su(1|1) sector of N=4 SYM

TL;DR

This paper analyzes the strong coupling behavior of anomalous dimensions in the su(1|1) sector of N=4 SYM, using integral equations and Neumann expansions to derive analytical and numerical results.

Contribution

It provides the first analytical derivation of the strong coupling expansion terms for the su(1|1) sector using Neumann methods and explores the sector-specific features.

Findings

Analytical expressions for the first two strong coupling terms.

Numerical results for higher-order corrections.

Identification of a singular integral equation at next-to-leading order.

Abstract

We consider the anomalous dimension of the fermionic highest states Tr(psi^L) in the su(1|1) sector of N=4 SYM at strong coupling. In the thermodynamical L->OO limit it is described by a BES-like integral equation recently proposed by Rej, Staudacher and Zieme. The strong coupling regime of this equation is analyzed numerically and analytically by Neumann expansion methods which have been developed for the sl(2) sector. We compute analytically the first two terms of the strong coupling expansion and present numerical results for the next correction. We illustrate various specific features valid for the su(1|1) sector. In particular, at next-to-leading order, we find and solve a singular integral equation describing the scaling continuum limit of the Neumann coefficients.