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

Abstract

Recently the Schur index of $\mathcal{N}=4$ 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.

15 pages. 1 figure

References in corpus (3)

• Applications of the Superconformal Index for Protected Operators and q-Hypergeometric Identities to N=1 Dual Theories
• The exact Schur index of $\mathcal{N}=4$ SYM
• ABJ Wilson loops and Seiberg Duality

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• The NS limit of the 5D Superconformal Index
• ADHM Wilson line defect indices
• S-duality of boundary lines in $\mathcal{N}=4$ SYM theories and supersymmetric indices
• $\mathcal{N}=4$ line defect correlators of type BCD
• Fermi-gas correlators of ADHM theory and triality symmetry
• Schur Connections: Chord Counting, Line Operators, and Indices