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

2024/09/24 by Robert de Mello Koch, Koch, Robert de Mello, Minkyoo Kim +3 · 4 citations
Computer Science · Mathematics · #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Holomorphic and Operator Theory #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · pdf · doi:10.48550/arxiv.2409.15751

openalex publication_date 2024/09/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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 For these operators, traditional techniques that work effectively in the planar limit are no longer applicable.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.

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