Supersymmetric black holes from ISO(3)U(1) F(4) gauged supergravity

Parinya Karndumri

doi:10.1140/epjc/s10052-025-13880-0

2023 Impact factor 4.2

Particles and Fields

Open Access

Eur. Phys. J. C (2025) 85: 158
https://doi.org/10.1140/epjc/s10052-025-13880-0

Regular Article - Theoretical Physics

Supersymmetric $A d S_{6}$ black holes from ISO(3) $\times$ $\times$ U(1) F(4) gauged supergravity

Parinya Karndumri^a

String Theory and Supergravity Group, Department of Physics, Faculty of Science, Chulalongkorn University, 254 Phayathai Road, Pathumwan, 10330, Bangkok, Thailand

^a parinya.ka@hotmail.com

Received: 2 December 2024
Accepted: 27 January 2025
Published online: 7 February 2025

Abstract

We study supersymmetric $A d S_{6}$ $$AdS_6$$ black holes from matter-coupled F(4) gauged supergravity coupled to four vector multiplets with $I S O (3) \times U (1)$ $ISO(3)\times U(1)$ gauge group. This gauged supergravity admits a maximally supersymmetric $A d S_{6}$ vacuum with $S O (3) \subset I S O (3)$ $SO(3)\subset ISO(3)$ symmetry. We find a number of new supersymmetric $A d S_{2} \times M_{4}$ $AdS_2\times \mathcal {M}_4$ solutions by performing topological twists along $M_{4}$ $\mathcal {M}_4$ . For $M_{4}$ $\mathcal {M}_4$ being a product of two Riemann surfaces $Σ \times \tilde{Σ}$ $\Sigma \times \widetilde{\Sigma }$ , we perform a twist by $S O (2) \times U (1)$ $SO(2)\times U(1)$ gauge fields and find $A d S_{2} \times Σ \times \tilde{Σ}$ $AdS_2\times \Sigma \times \widetilde{\Sigma }$ solutions for at least one of the Riemann surface being negatively curved. For $M_{4}$ $\mathcal {M}_4$ being a Kahler four-cycle $M_{K 4}$ $\mathcal {M}_{\text {K}4}$ , a twist by $S O (2) \times U (1)$ $SO(2)\times U(1)$ gauge fields leads to $A d S_{2} \times M_{K 4}^{-}$ $AdS_2\times \mathcal {M}_{\text {K}4}^-$ solutions for negatively curved $M_{K 4}$ $\mathcal {M}_{\text {K}4}$ . Finally, performing a twist by turning on SO(3) gauge fields in the case of $M_{4}$ $\mathcal {M}_4$ being a Cayley four-cycle $M_{C 4}$ $\mathcal {M}_{\text {C}4}$ also leads to $A d S_{2} \times M_{C 4}^{-}$ $AdS_2\times \mathcal {M}_{\text {C}4}^-$ solutions for negatively curved $M_{C 4}$ $\mathcal {M}_{\text {C}4}$ . We give numerical black hole solutions interpolating between all of these $A d S_{2} \times M_{4}$ $AdS_2\times \mathcal {M}_4$ near horizon geometries and the asymptotically locally $A d S_{6}$ $$AdS_6$$ vacuum. It is also possible to uplift all of these solutions to type IIB theory via consistent truncations on $S^{2} \times Σ$ $S^2\times \Sigma$ leading to a new class of supersymmetric $A d S_{2} \times M_{4} \times S^{2} \times Σ$ $AdS_2\times \mathcal {M}_4\times S^2\times \Sigma$ solutions.

© The Author(s) 2025

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