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

2024/10/10 by Robert de Mello Koch, Minkyoo Kim, Augustine Larweh Mahu · 5 citations
Computer Science · Mathematics · #Holomorphic and Operator Theory #Mathematical functions and polynomials #Matrix Theory and Algorithms

paper · doi:10.1142/s0217751x24300035

openalex publication_date 2024/10/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/25

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 For these operators, traditional techniques that work effectively in the planar limit are no longer applicable.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

Citations

• A planar diagram theory for strong interactions

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• Violation of S-duality in classical Q-cohomology
• Gauge Invariants at Arbitrary N and Trace Relations
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• From Symmetry to Structure: Gauge-Invariant Operators in Multi-Matrix Quantum Mechanics

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