Giant Graviton Expansions for the Line Operator Index

Abstract

Abstract We discuss giant graviton expansions for the Schur index of ${\cal N}=4$  $U(N)$ SYM with the insertion of Wilson lines of the fundamental and antifundamental representations. We first propose a double-sum giant graviton expansion and numerically confirm that it correctly reproduces the line operator index. We also find that it reduces to a simple-sum expansion when we treat the index as a Taylor series with respect to a specific fugacity.