Fusion hierarchies for N = 4 superYang-Mills theory

TL;DR

This paper develops a mathematical framework using fusion hierarchies and Bethe ansatz techniques to analyze the spectral problem of N=4 super Yang-Mills theory, providing new functional equations for transfer matrices.

Contribution

It introduces a novel approach to construct transfer matrix eigenvalues and reduces an infinite hierarchy to a finite set of integral relations and functional equations.

Findings

Derived finite functional equations for transfer matrix eigenvalues.

Reduced infinite fusion hierarchy to a manageable finite set.

Provided a new analytical method for spectral analysis in supersymmetric gauge theories.

Abstract

We employ the analytic Bethe Anzats to construct eigenvalues of transfer matrices with finite-dimensional atypical representations in the auxiliary space for the putative long-range spin chain encoding anomalous dimensions of all composite single-trace gauge invariant operators of the maximally supersymmetric Yang-Mills theory. They obey an infinite fusion hierarchy which can be reduced to a finite set of integral relations for a minimal set of transfer matrices. This set is used to derive a finite systems of functional equations for eigenvalues of nested Baxter polynomials.