BPS black hole horizons from massive IIA

TL;DR

The paper addresses how BPS black hole horizons in four-dimensional ${\mathcal N}=2$ gauged supergravity descend from massive IIA on ${S^6}$ with a dyonic ${\rm ISO}(7)$ gauging, focusing on whether horizon data are uniquely fixed or admit continuous freedom. It extends the attractor mechanism to truncations with varying numbers of vector and hypermultiplets, showing that adding hypermultiplets beyond the universal one does not introduce new horizon configurations, while adding vector multiplets yields a four-parameter family of hyperbolic or spherical horizons, including a massive IIA STU-like model. Horizon data are expressed in terms of horizon scalars $(z_h^i,z_h^j)$ and gauging parameters $(g,m)$, with entropy given by $s=\frac{V_{\mathrm{eff}}(z_h^i,z_h^j)}{4}$; the STU-like model provides a natural arena for holographic tests of massive IIA on $S^6$/SYM-CS beyond AdS. These results set the stage for future holographic interpretations and microstate counting in non-AdS backgrounds within massive IIA frameworks.

Abstract

The maximal four-dimensional supergravity with a dyonic ISO(7) gauging that arises from the reduction of massive IIA on a six-sphere has recently been shown to accommodate static BPS black holes with hyperbolic horizons. When restricted to the N=2 subsector that retains one vector multiplet and the universal hypermultiplet, the attractor mechanism was shown to fix both the vector charges and the scalar fields at the horizon to a unique configuration in terms of the gauging parameters. In order to assess the (non-)uniqueness of BPS black hole horizons from massive IIA, we extend the study of the attractor mechanism to other N=2 subsectors including additional matter multiplets. We note that, while extending the hypermultiplet sector does not modify the set of solutions to the attractor equations, the inclusion of additional vector multiplets results in new hyperbolic/spherical horizons containing free parameters. The model with three vector multiplets and the universal hypermultiplet, which is the massive IIA analogue of the STU-model from M-theory, may play a relevant role in massive IIA holography.

Figures (2)

• Figure 1: Horizon configurations as a function of the deformation parameter $\,\epsilon\,$ when $\,\lambda=+$. There is a transition from hyperbolic to spherical horizon at $\,|\epsilon_{\textrm{crit}}| = 3^{1/2} \, 2^{-1/4}$.
• Figure 2: Horizon configurations as a function of the deformation parameter $\,\epsilon\,$ when $\,\lambda=-$. There is a transition from hyperbolic to spherical horizon at $\,\epsilon_{\textrm{crit}} \approx 0.7304$.