Restricted Schur Polynomials and Finite N Counting

TL;DR

This paper explores the relationship between restricted Schur polynomials and operators in N=4 SYM, focusing on their finite N counting and their role as orthonormal operators in the gauge-string correspondence.

Contribution

It clarifies the connection between restricted Schur polynomials and previously studied operators, and examines their finite N counting properties.

Findings

Established the relationship between restricted Schur polynomials and Brown, Heslop, and Ramgoolam's operators.

Analyzed finite N counting of restricted Schur polynomials.

Discussed their role as orthonormal operators in the gauge-string duality.

Abstract

Restricted Schur polynomials have been posited as orthonormal operators for the change of basis from N=4 SYM to type IIB string theory [1,2,3,4]. In this letter we briefly expound the relationship found between the restricted Schurs and the operators found by Brown, Heslop and Ramgoolam in [5]. We then briefly examine the finite N counting of the restricted Schur polynomials.