The ${\cal N}=4$ Schur index with Polyakov loops

TL;DR

This paper applies the Fermi-gas approach to evaluate the ${ m{Sch}}$ur index of ${ m{ extbf{N}}}=4$ SYM with Polyakov loops, providing explicit large $N$ results for various representations and enriching the index with loop operators.

Contribution

It extends the Fermi-gas formalism to include Polyakov loops in the ${ m{ extbf{N}}}=4$ SYM Schur index, offering explicit large $N$ results for different representations.

Findings

Explicit large $N$ results for the Schur index with Polyakov loops.

Inclusion of Wilson loops as insertions in the matrix model.

Application of the Fermi-gas approach to enriched index calculations.

Abstract

Recently the Schur index of ${\cal N}=4$ SYM was evaluated in closed form to all orders including exponential corrections in the large $N$ expansion and for fixed finite $N$. This was achieved by identifying the matrix model which calculates the index with the partition function of a system of free fermions on a circle. The index can be enriched by the inclusion of loop operators and the case of Wilson loops is particularly easy, as it amounts to inserting extra characters into the matrix model. The Fermi-gas approach is applied here to this problem, the formalism is explored and explicit results at large $N$ are found for the fundamental as well as a few other symmetric and antisymmetric representations.