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BPS black holes from massive IIA on S$^6$

Adolfo Guarino, Javier Tarrio

TL;DR

This work constructs and analyzes BPS black hole solutions in a four-dimensional $\mathcal{N}=2$ gauged supergravity with a dyonic abelian gauging, arising from the massive IIA theory reduced on $\mathrm{S}^6$. The model sits in the SU(3)-invariant subsector of maximal ISO(7) gauged supergravity and couples a vector multiplet to the universal hypermultiplet, with a tensor field activated by magnetic gaugings. The authors derive the full set of first-order BPS equations for static, spherically/hyperbolic symmetric configurations and exhibit a two-parameter family of flows that interpolate from a unique IR $\mathrm{AdS}_{2} \times \mathrm{H}^{2}$ horizon to a UV domain-wall description $\mathrm{DW}_{4}$ of the D2-brane, with running hyperscalars along the flow. They also uncover charged $\mathrm{AdS}_{4}$-like and non-relativistic UV solutions as special corners of the parameter space. The results illuminate holographic connections between D2-brane physics in massive IIA and AdS$_{2}$-based black hole horizons, demonstrating a rich landscape of BPS flows including non-trivial UV scalars and tensor dynamics.

Abstract

We present BPS black hole solutions in a four-dimensional $\mathcal{N}=2$ supergravity with an abelian dyonic gauging of the universal hypermultiplet moduli space. This supergravity arises as the SU(3)-invariant subsector in the reduction of massive IIA supergravity on a six-sphere. The solutions are supported by non-constant scalar, vector and tensor fields and interpolate between a unique $\textrm{AdS}_{2} \,\times\, \textrm{H}^2$ geometry in the near-horizon region and the domain-wall DW$_{4}$ (four-dimensional) description of the D2-brane at the boundary. Some special solutions with charged AdS$_{4}$ or non-relativistic scaling behaviours in the ultraviolet are also presented.

BPS black holes from massive IIA on S$^6$

TL;DR

This work constructs and analyzes BPS black hole solutions in a four-dimensional gauged supergravity with a dyonic abelian gauging, arising from the massive IIA theory reduced on . The model sits in the SU(3)-invariant subsector of maximal ISO(7) gauged supergravity and couples a vector multiplet to the universal hypermultiplet, with a tensor field activated by magnetic gaugings. The authors derive the full set of first-order BPS equations for static, spherically/hyperbolic symmetric configurations and exhibit a two-parameter family of flows that interpolate from a unique IR horizon to a UV domain-wall description of the D2-brane, with running hyperscalars along the flow. They also uncover charged -like and non-relativistic UV solutions as special corners of the parameter space. The results illuminate holographic connections between D2-brane physics in massive IIA and AdS-based black hole horizons, demonstrating a rich landscape of BPS flows including non-trivial UV scalars and tensor dynamics.

Abstract

We present BPS black hole solutions in a four-dimensional supergravity with an abelian dyonic gauging of the universal hypermultiplet moduli space. This supergravity arises as the SU(3)-invariant subsector in the reduction of massive IIA supergravity on a six-sphere. The solutions are supported by non-constant scalar, vector and tensor fields and interpolate between a unique geometry in the near-horizon region and the domain-wall DW (four-dimensional) description of the D2-brane at the boundary. Some special solutions with charged AdS or non-relativistic scaling behaviours in the ultraviolet are also presented.

Paper Structure

This paper contains 12 sections, 82 equations, 4 figures, 1 table.

Table of Contents

  1. Motivation and outlook
  2. $\mathcal{N}=2$ supergravity with abelian gaugings from massive IIA
  3. BPS equations in dyonically gauged $\,\mathcal{N}=2\,$ supergravity
  4. Field ansatz and gauge fixing
  5. First-order BPS equations
  6. Black holes and BPS flows
  7. Near-horizon region and attractor equations
  8. Asymptotically AdS$_{4}$ solutions with charges
  9. BPS flows from the $\,\mathrm{DW}_4\,$ to $\textrm{AdS}_{2} \times \textrm{H}^{2}$
  10. Non-relativistic UV asymptotics
  11. Equations of motion
  12. UV expansion around DW$_{4}$

Figures (4)

  • Figure 1: Plot of the two-dimensional parameter space $\,(c_{1},c_{2})\,$ of BPS solutions (shaded area) interpolating between the $\,{\textrm{AdS}_{2} \times \textrm{H}^{2}}\,$ geometry in the IR and the $\,\mathrm{DW}_4\,$ solution in the UV.
  • Figure 2: Plots of the metric functions, scalars and tensor field profiles as a function of the radial coordinate. The numerical integration was performed with $\,(c_1,c_2)=(-1,-1)\,$.
  • Figure 3: Plots of the logarithmic derivatives of the metric functions. The red, dashed line corresponds to the metric functions in the asymptotically AdS$_{4}$ solution (\ref{['metric_sol_analytic']}). The blue, straight curve was produced numerically with $\,(c_1,c_2)=(0,-10^{-8})\,$.
  • Figure 4: Plots of the scalars $\,e^\phi\,$ (blue, straight line), $\,e^\varphi\,$ (brown, dashed line) and $\,-\chi\,$ (green, dotted line), as well as of the phase $\,-\beta$, as a function of the radial coordinate for a solution with $\,(c_1,c_2)=(1.138,-1.68)\,$.