A pedagogical introduction to restricted Schur polynomials with applications to heavy operators

TL;DR

This paper introduces restricted Schur polynomials as a powerful tool for analyzing heavy operators in gauge theories, especially relevant for understanding microstates of 1/16-BPS black holes beyond the planar limit.

Contribution

It provides a pedagogical development of restricted Schur polynomial methods tailored for finite N effects in heavy operators, with applications to black hole microstate analysis.

Findings

Restricted Schur polynomials effectively handle finite N trace relations.

The methods facilitate analysis of heavy operators beyond the planar approximation.

Application to 1/16-BPS black hole microstates is outlined.

Abstract

Recent advances in the study of microstates for 1/16-BPS black holes have inspired renewed interest in the analysis of heavy operators. For these operators, traditional techniques that work effectively in the planar limit are no longer applicable. Methods that are sensitive to finite N effects are required. In particular, trace relations that connect different multi-trace operators must be carefully considered. A powerful approach to tackling this challenge, which utilizes the representation theory of the symmetric group, is provided by restricted Schur polynomials. In this review, we develop these methods with the goal of providing the background needed for their application to 1/16-BPS black holes.