Rotating multi-charge spindles and their microstates

Abstract

Some AdS3 × M7 type IIB vacua have been recently proposed to arise from D3-branes wrapped on a spindle, a sphere with conical singularities at the poles. We explicitly construct a generalization of these solutions corresponding to a class of electrically charged and rotating supersymmetric black strings in AdS5 × S5 with general magnetic fluxes on the spindle. We then perform a counting of their microstates using the charged Cardy formula. To this purpose, we derive the general form of the anomaly polynomial of the dual $$ \mathcal{N} $$ N = (0, 2) CFT in two dimensions and we show that it can be obtained via a simple gluing procedure.

M5-branes wrapped on a spindle

“…Notice that we are working in a specifc gauge for the "flavour" symmetry gauge field, A1 − A2, that is given by the original supergravity solution. This is analogous to the analysis of D3-branes wrapped on a spindle in[10], whereas in the same setting other gauge choices were analysed in[9], leading to the same final result for the central charge.…”

“…In fact further interesting examples have already appeared. In [9,10] the solutions of [6] were generalized from minimal D = 5 gauged supergavity to the STU model, which has three Abelian gauge fields. The solutions can be uplifted on the five-sphere to obtain solutions of type IIB supergravity describing D3-branes wrapping the spindle, which are again completely regular, and were first constructed in [7].…”

“…Furthermore the central charge of the d = 2 SCFT obtained from the gravity solution agrees exactly with the associated field theory calculation using the anomaly polynomial of N = 4 SYM theory in d = 4. In the solutions describing D3-branes wrapped on spindles in both [6] and [9,10], supersymmetry is not being realized by the topological twist; for example, it was shown by explicit construction in [6] that the Killing spinors are not constant on Σ, and moreover are in fact sections of non-trivial bundles over Σ.…”

Supersymmetric black holes with spiky horizons

“…, also called spindle (see [29][30][31] for a list of recent references on this topic). This space is topologically a 2-sphere, but with conical singularities at the poles, characterized by deficit angles 2π(1 − 1/n 1,2 ), with n 1,2 two coprime positive integers.…”

The topologically twisted index of $$ \mathcal{N} $$ = 4 SU(N) Super-Yang-Mills theory and a black hole Farey tail

“…Similarly, one may extend our analysis to recently constructed spindle solutions where the Riemann surface Σ g used in this paper is replaced with a two-dimensional orbifold known as a spindle [61,62]. In this case, however, a dual twisted index has not yet been explored enough and therefore a direct comparison between a canonical partition function and a gravitational partition function could be more demanding.…”