Supersymmetric extensions of Kac-Moody boundary conditions in AdS$_3$ gravity
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arXiv
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| Autori principali: | , , , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866909936466788352 |
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| author | Banerjee, Nabamita Bhutra, Vedant Dutta, Suvankar Kundu, Soumava |
| author_facet | Banerjee, Nabamita Bhutra, Vedant Dutta, Suvankar Kundu, Soumava |
| contents | We extend the Kac-Moody (KM) boundary conditions of AdS$_3$ gravity by incorporating fermionic fields. For $\mathcal{N}=(1,1)$ AdS$_3$ supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the super-Miura map between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2510_21678 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Supersymmetric extensions of Kac-Moody boundary conditions in AdS$_3$ gravity Banerjee, Nabamita Bhutra, Vedant Dutta, Suvankar Kundu, Soumava High Energy Physics - Theory We extend the Kac-Moody (KM) boundary conditions of AdS$_3$ gravity by incorporating fermionic fields. For $\mathcal{N}=(1,1)$ AdS$_3$ supergravity, we show that there are two possible ways to implement the fermionic extension. In the first, the extended KM boundary conditions are related to the standard super-Virasoro (VS) boundary conditions through a large gauge transformation realized by the super-Miura map between fields and chemical potentials, establishing a supersymmetric generalization of the KM-VS correspondence. In the second, a more general boundary configuration leads to strong constraints on the fermionic chemical potentials, yet offers a much richer asymptotic structure. It provides us a novel realization of the extended Kac-Moody algebra, and a geometric interpretation in terms of folds in the relativistic free-fermion droplet. Finally, we quantize the latter theory by promoting the classical Poisson brackets to (anti-)commutators, construct the corresponding Hilbert space, and show that the resulting spectrum contains only bosonic soft excitations, with no additional fermionic soft modes. |
| title | Supersymmetric extensions of Kac-Moody boundary conditions in AdS$_3$ gravity |
| topic | High Energy Physics - Theory |
| url | https://arxiv.org/abs/2510.21678 |