Finite N indices from branes and negative branes

Finite-N effects in large-N gauge theories, such as trace relations, are expected to be holographically dual to non-perturbative phenomena in string theory, such as Giant Graviton branes. A convenient setting to study these effects are supersymmetric indices of U(N) gauge theories. The finite-N indices can be reproduced by a series of corrections to the infinite-N result, known as the Giant Graviton expansion.

In this talk I will present a generalization of the Molien-Weyl formula computing generating functions of invariants of supergroups U(N|M), which arise as gauge groups of brane/negative brane systems in string theory. The formula leads to a new expansion relating finite-N and infinite-N indices of U(N) gauge theories. I will comment on its relation to Murthy’s Giant Graviton expansion and suggest a physical interpretation in terms of branes and negative branes. This talk is based on arXiv:2509.20451 and work in progress with Davide Gaiotto.

In person and online: