Supergroup Invariants and the Brane/Negative Brane Expansion
Fuente:
arXiv
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| Formato: | Preprint |
| Publicado: |
2025
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| _version_ | 1866911176412102656 |
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| author | Budzik, Kasia |
| author_facet | Budzik, Kasia |
| contents | We propose a Molien--Weyl-type formula computing generating functions of invariants of supergroups $U(N|M)$, i.e. polynomials in supertraces, which arise as gauge groups of brane/negative brane systems in string theory. We either prove or numerically verify the formula in various examples. The formula further leads to a new expansion relating finite-$N$ and infinite-$N$ indices of $U(N)$ gauge theories. We comment on its relation to Murthy's Giant Graviton expansion, for which we suggest a physical interpretation in terms of ``Koszul dual" branes and negative branes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_20451 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supergroup Invariants and the Brane/Negative Brane Expansion Budzik, Kasia High Energy Physics - Theory Mathematical Physics We propose a Molien--Weyl-type formula computing generating functions of invariants of supergroups $U(N|M)$, i.e. polynomials in supertraces, which arise as gauge groups of brane/negative brane systems in string theory. We either prove or numerically verify the formula in various examples. The formula further leads to a new expansion relating finite-$N$ and infinite-$N$ indices of $U(N)$ gauge theories. We comment on its relation to Murthy's Giant Graviton expansion, for which we suggest a physical interpretation in terms of ``Koszul dual" branes and negative branes. |
| title | Supergroup Invariants and the Brane/Negative Brane Expansion |
| topic | High Energy Physics - Theory Mathematical Physics |
| url | https://arxiv.org/abs/2509.20451 |