Giant graviton expansion for general Wilson line operator indices

TL;DR

This paper introduces a novel giant graviton expansion method for calculating Wilson line operator indices in various representations, linking symmetric polynomials to string worldsheet structures and validating the approach with numerical tests.

Contribution

It presents a new expansion framework for Wilson line indices using giant gravitons and symmetric polynomials, extending previous methods and providing a unified computational approach.

Findings

The formula aligns with known results.

Numerical tests confirm the validity of the expansion.

Provides a geometric interpretation of line operators.

Abstract

We propose a giant graviton expansion for Wilson line operator indices in general representations. The inserted line operators are specified by power sum symmetric polynomials $p_\lambda$ labeled by partitions $\lambda$. We interpret the partitions as the structure of fundamental string worldsheets wrapping around the temporal circle. The strings may or may not end on giant gravitons, and by summing the contributions from all brane configurations consistent with the specified partitions, we obtain the finite $N$ line operator index. The proposed formula is consistent with known results and passes highly non-trivial numerical tests.