Finite N indices and the giant graviton expansion

The superconformal index of N = 4 super-Yang Mills theory with U(N) gauge group can be written as a matrix integral over the gauge group. Recently, Murthy demonstrated that this integral can be reexpressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for the case of a single giant graviton. Here we give similar explicit formulae for an arbitrary number, m = 1, of giant gravitons. We provide 1/2 and 1/16 BPS index examples up to the order where three giant gravitons contribute and demonstrate that the expansion of the matrix integral differs from the giant graviton expansion computed in the supergravity dual. This shows that the giant graviton expansion is not necessarily unique once two or more giant gravitons start appearing.

Automated summary

It has been shown that the superconformal index of N=4 super-Yang Mills theory can be represented as a matrix integral. Recently, Murthy demonstrated that this integral can be expressed as a sum of terms corresponding to a giant graviton expansion of the index, and provided an explicit formula for a single giant graviton. In this study, similar explicit formulae are given for an arbitrary number of giant gravitons. Examples of 1/2 and 1/16 BPS indices are provided, and it is shown that the expansion of the matrix integral differs from the giant graviton expansion computed in the supergravity dual, indicating that the giant graviton expansion is not necessarily unique once two or more giant gravitons start appearing.