Nesting and Dressing

TL;DR

This paper derives an all-loop integral equation for the anomalous dimensions of certain operators in N=4 SYM using an asymptotic nested Bethe ansatz, revealing insights into the origin of the dressing phase in the AdS/CFT correspondence.

Contribution

It introduces a unified integral equation for all-loop anomalous dimensions, incorporating the dressing phase and revealing its potential origin from auxiliary Bethe roots.

Findings

Derived a single effective integral equation for the thermodynamic limit.

Included the phase factor for the S-matrix in the analysis.

Suggested the dressing phase arises from auxiliary Bethe roots.

Abstract

We compute the anomalous dimensions of field strength operators Tr F^L in N=4 SYM from an asymptotic nested Bethe ansatz to all-loop order. Starting from the exact solution of the one-loop problem at arbitrary L, we derive a single effective integral equation for the thermodynamic limit of these dimensions. We also include the recently proposed phase factor for the S-matrix of the planar AdS/CFT system. The terms in the effective equation corresponding to, respectively, the nesting and the dressing are structurally very similar. This hints at the physical origin of the dressing phase, which we conjecture to arise from the hidden presence of infinitely many auxiliary Bethe roots describing a non-trivial "filled" structure of the theory's BPS vacuum. We finally show that the mechanism for creating effective nesting/dressing kernels is quite generic by also deriving the integral equation for the all-loop dimension of a certain one-loop so(6) singlet state.