Exact Path Integral Methods in Supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ Backgrounds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866908891143471104 |
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| author | Castellano, Alberto Montella, Carmine Zatti, Matteo |
| author_facet | Castellano, Alberto Montella, Carmine Zatti, Matteo |
| contents | We determine the exact functional determinants of charged, massive spin-0 and spin-$\frac12$ particles in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric and magnetic fields. This is achieved using Schwinger proper-time formalism, which allows us to derive the full non-perturbative effective action in the 1-loop and constant background field approximations. We then specialize the computation to supersymmetric settings and we obtain the effective action for a 4d $\mathcal{N}=2$ BPS massive hypermultiplet in a supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ spacetime. This setup can be seen to be equivalent to the near-horizon geometry of a BPS black hole which solves the attractor equations of 4d $\mathcal{N}=2$ supergravity. Our results provide a necessary intermediate step for the evaluation of the quantum-corrected black hole partition function. We also comment on the relation with the celebrated Gopakumar-Vafa integral representation. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_15730 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Exact Path Integral Methods in Supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ Backgrounds Castellano, Alberto Montella, Carmine Zatti, Matteo High Energy Physics - Theory General Relativity and Quantum Cosmology We determine the exact functional determinants of charged, massive spin-0 and spin-$\frac12$ particles in $\text{AdS}_2\times \mathbf{S}^2$ backgrounds threaded by constant electric and magnetic fields. This is achieved using Schwinger proper-time formalism, which allows us to derive the full non-perturbative effective action in the 1-loop and constant background field approximations. We then specialize the computation to supersymmetric settings and we obtain the effective action for a 4d $\mathcal{N}=2$ BPS massive hypermultiplet in a supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ spacetime. This setup can be seen to be equivalent to the near-horizon geometry of a BPS black hole which solves the attractor equations of 4d $\mathcal{N}=2$ supergravity. Our results provide a necessary intermediate step for the evaluation of the quantum-corrected black hole partition function. We also comment on the relation with the celebrated Gopakumar-Vafa integral representation. |
| title | Exact Path Integral Methods in Supersymmetric $\text{AdS}_2\times \mathbf{S}^2$ Backgrounds |
| topic | High Energy Physics - Theory General Relativity and Quantum Cosmology |
| url | https://arxiv.org/abs/2603.15730 |