Fine structure of the asymptotic expansion of cyclic integrals

TL;DR

This paper provides explicit formulas for functionals acting on symmetric functions, advancing the understanding of the asymptotic expansion of cyclic integrals crucial for analyzing correlation functions in integrable models.

Contribution

It introduces explicit formulas for the action of functionals on symmetric functions within the asymptotic expansion of cyclic integrals, aiding long-distance correlation analysis.

Findings

Explicit formulas for functional actions derived

Enhanced understanding of cyclic integral asymptotics

Facilitates computation of correlation function behavior

Abstract

The asymptotic expansion of $n$-dimensional cyclic integrals was expressed as a series of functionals acting on the symmetric function involved in the cyclic integral. In this article, we give an explicit formula for the action of these functionals on a specific class of symmetric functions. These results are necessary for the computation of the O(1) part in the long-distance asymptotic behavior of correlation functions in integrable models.