Spindle black holes in AdS4 × SE7

Abstract

We construct new classes of supersymmetric AdS2 × Σ solutions of 4d gauged supergravity in presence of charged hypermultiplet scalars, with Σ the complex weighted projective space known as a spindle. These solutions can be viewed as near-horizon geome- tries of asymptotically Anti de-Sitter (AdS4) black holes with magnetic fluxes that admit embedding in 11d on Sasaki-Einstein (SE7) manifolds, which renders them of holographic interest. We show that in each case the Bekenstein-Hawking entropy follows from the procedure of gluing two gravitational blocks, ultimately determined by SE7 data. This allows us to establish the general form of the gravitational blocks in gauged 4d $$ \mathcal{N} $$ N = 2 supergravity with charged scalars and massive vectors. Holographically, our results provide a large N answer for the spindle index with anti-twist and additional mesonic or baryonic fluxes of a number of $$ \mathcal{N} $$ N = 2 Chern-Simons-matter theories.

M5-branes wrapped on a spindle

“…Some of the simplest examples of GK geometries where the metrics are explicitly known have been recently revisited and interpreted as describing a situation in which branes are wrapped on two-dimensional orbifolds known as spindles, originally found for D3 branes [14]. Ever since, solutions describing branes wrapping spindles have been found in a large variety of examples [14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32] and generalized to other two- [33][34][35][36][37][38][39][40][41][42] and higher-dimensional [43][44][45][46][47][48][49] orbifolds.…”

D3-branes and M5-branes wrapped on a topological disc

“…The expressions of these off-shell quantities, namely the"gravitational blocks", [4], were conjectured and proved to reproduce the corresponding observables, e.g., the Bekenstein-Hawking entropies, central charges, and free energies. Later, the gravitational blocks for solutions with orbifold singularities, i.e., spindle, were proposed, [5,6], and proved to calculate the duals of partition functions, [7,8,9,10,11,12]. See [13,14] also for an approach from string and M-theory.…”

Localization and attraction

“…It would be interesting to study other models that can also be uplifted to string/Mtheory. For example, one should be able to make contact with the solutions discussed in [83] and [84] with S 2 and spindle horizons, respectively. More generally, it would certainly be of interest to extend our analysis to supergravity theories with arbitrary hypermultiplets.…”