Analytic continuation for giant gravitons

TL;DR

This paper develops a systematic method for analytic continuation of superconformal indices related to giant gravitons, enabling the calculation of indices across different brane theories through variable transformations.

Contribution

It introduces a novel prescription for analytic continuation of superconformal indices, facilitating the computation of indices for M5- and M2-brane theories from each other.

Findings

The prescription successfully passes numerical checks in example cases.

It allows calculation of M5-brane indices from M2-brane indices and vice versa.

The method handles contributions from coincident giant gravitons wrapped around a cycle.

Abstract

We investigate contributions of giant gravitons to the superconformal index. We concentrate on coincident giant gravitons wrapped around a single cycle, and each contribution is obtained by a certain variable change for fugacities from the index of the worldvolume theory on the giant gravitons. Because we treat the index as a series of fugacities and the variable change relates different convergence regions, we need an analytic continuation before summing up such contributions. We propose a systematic prescription for the continuation. Although our argument is based on some unproved assumptions, it passes non-trivial numerical checks for some examples. With the prescription we can calculate the indices of the M5-brane theories from those of the M2-brane theories, and vice versa.