PIRSA:25110060

Supergroup invariants and finite N indices

Budzik, K. (2025). Supergroup invariants and finite N indices. Perimeter Institute. https://pirsa.org/25110060

Budzik, Kasia. Supergroup invariants and finite N indices. Perimeter Institute, Nov. 05, 2025, https://pirsa.org/25110060 

          @misc{ pirsa_PIRSA:25110060,
            doi = {10.48660/25110060},
            url = {https://pirsa.org/25110060},
            author = {Budzik, Kasia},
            keywords = {Mathematical physics},
            language = {en},
            title = {Supergroup invariants and finite N indices},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110060 see, \url{https://pirsa.org}}
          }

Kasia Budzik Harvard University

Talk numberPIRSA:25110060
DOI10.48660/25110060
Collection
Talk Type Conference
Subject

Abstract

Finite-N effects in large-N gauge theories, such as trace relations, are expected to be dual to non-perturbative phenomena in quantum gravity, such as Giant Graviton branes. A convenient setting to study these effects are supersymmetric indices of U(N) invariants. 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 ``Koszul dual" branes and negative branes. This talk is based on arXiv:2509.20451 and work in progress with Davide Gaiotto.