Rotating Restricted Schur Polynomials

TL;DR

This paper develops a method to exactly determine how symmetry generators act on restricted Schur polynomials, advancing the understanding of non-perturbative effects in large N super Yang-Mills theory.

Contribution

It introduces a new approach to compute the exact action of symmetry generators on restricted Schur polynomials beyond small perturbations.

Findings

Exact symmetry generator actions derived for restricted Schur polynomials.

Framework applicable to non-perturbative regimes in super Yang-Mills theory.

Enhances understanding of large N, non-planar limits in gauge theories.

Abstract

Large $N$ but non-planar limits of ${\cal N}=4$ super Yang-Mills theory can be described using restricted Schur polynomials. Previous investigations demonstrate that the action of the one loop dilatation operator on restricted Schur operators, with classical dimension of order $N$ and belonging to the $su(2)$ sector, is largely determined by the $su(2)$ ${\cal R}$ symmetry algebra as well as structural features of perturbative field theory. Studies presented so far have used the form of ${\cal R}$ symmetry generators when acting on small perturbations of half-BPS operators. In this article, as a first step towards going beyond small perturbations of the half-BPS operators, we explain how the exact action of symmetry generators on restricted Schur polynomials can be determined.