Extended Y-system for the $AdS_5/CFT_4$ correspondence

TL;DR

This paper investigates the analytic structure of Y functions in the AdS5/CFT4 correspondence, deriving TBA equations from an extended Y-system with discontinuity relations, providing a foundational set of local functional constraints.

Contribution

It introduces an extended Y-system incorporating discontinuity relations, enabling derivation of TBA equations with dressing factors from fundamental functional constraints.

Findings

Y-functions' analytic properties are characterized.

TBA equations are derived from the extended Y-system.

Discontinuity relations facilitate transformation into integral equations.

Abstract

We study the analytic properties of the $AdS_5/CFT_4$ Y functions. It is shown that the TBA equations, including the dressing factor, can be obtained from the Y-system with some additional information on the square-root discontinuities across semi-infinite segments in the complex plane. The Y-system extended by the discontinuity relations constitutes a fundamental set of local functional constraints that can be easily transformed into integral form through Cauchy's theorem.