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

Abstract

Recent advances in the study of microstates for [Formula: see text]-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 For these operators, traditional techniques that work effectively in the planar limit are no longer applicable.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 paper, we develop these methods with the goal of providing the background needed for their application to [Formula: see text]-BPS black holes.