Hybrid NLIE for the Mirror AdS_5 x S^5

TL;DR

This paper develops hybrid nonlinear integral equations for the mirror AdS_5 x S^5 model by linearizing the T-system, introducing auxiliary variables to simplify the complex relations in the integrable structure.

Contribution

It introduces a novel derivation of hybrid NLIEs for the mirror AdS_5 x S^5, connecting TQ-relations with auxiliary variables to simplify the integrable model analysis.

Findings

Derived two sets of hybrid NLIEs for the model

Connected TQ-relations with auxiliary variables in the A_1 type

Simplified the analysis of the integrable structure

Abstract

We revisit the derivation of hybrid nonlinear integral equations of the XXX model starting from the linearization of the T-system related to spinon variables. We obtain two sets of equations, corresponding to two linearly independent solutions of A_1 TQ-relation. Recalling that the TQ-relations in the horizontal strips of the su(2|4|2)-hook is of A_1 type, we replace the corresponding Y-functions by a finite number of auxiliary variables.