Wronskian Solution for AdS/CFT Y-system

TL;DR

This paper derives a Wronskian-based solution to the quantum Y-system in AdS/CFT, enabling a more explicit characterization of the spectrum of anomalous dimensions through integrability techniques.

Contribution

It introduces a Wronskian determinant approach to solve the quantum Y-system for AdS/CFT, advancing the understanding of the spectrum of operators.

Findings

Explicit asymptotic form of Q-functions for large operators

Symmetries and analyticity properties of Q-functions established

Potential for generalization to finite size operators discussed

Abstract

Using the discrete Hirota integrability we find the general solution of the full quantum Y-system for the spectrum of anomalous dimensions of operators in the planar AdS5/CFT4 correspondence in terms of Wronskian-like determinants parameterized by a finite number of Baxter's Q-functions. We consider it as a useful step towards the construction of a finite system of non-linear integral equations (FiNLIE) for the full spectrum. The explicit asymptotic form of all the Q-functions for the large size operators is presented. We establish the symmetries and the analyticity properties of the asymptotic Q-functions and discuss their possible generalization to any finite size operators.