We provide a first principles derivation of the microscopic entropy of a very general class of supersymmetric, rotating, and accelerating black holes in <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math>. This is achieved by analyzing the large-<math><mi>N</mi></math> limit of the spindle index and completes the construction of the first example of a holographic duality involving supersymmetric field theories defined on orbifolds with conical singularities.

Italy

Edoardo Colombo

United Kingdom

Seyed Morteza Hosseini

Dario Martelli

Antonio Pittelli

Alberto Zaffaroni

Microstates of Accelerating and Supersymmetric <math><mrow><msub><mrow><mi>AdS</mi></mrow><mrow><mn>4</mn></mrow></msub></mrow></math> Black Holes from the Spindle Index

In a previous paper two of us (D.M. and A.Z.) proposed that a vast class of gravitational extremization problems in holography can be formulated in terms of the equivariant volume of the internal geometry, or of the cone over it. We substantiate this claim by analysing supergravity solutions corresponding to branes partially or totally wrapped on a four-dimensional orbifold, both in M-theory as well as in type II supergravities. We show that our approach recovers the relevant gravitational central charges/free energies of several known supergravity solutions and can be used to compute these also for solutions that are not known explicitly. Moreover, we demonstrate the validity of previously conjectured gravitational block formulas for M5 and D4 branes. In the case of M5 branes we make contact with a recent approach based on localization of equivariant forms, constructed with Killing spinor bilinears.

Federico Faedo

Equivariant volume extremization and holography

We study the superconformal index of   <math> <mi>N</mi> </math>  $$ \mathcal{N} $$  = 1 quiver theories at large-N for general values of electric charges and angular momenta, using both the Bethe Ansatz formulation and the more recent elliptic extension method. We are particularly interested in the case of unequal angular momenta, J 1 ≠ J 2, which has only been partially considered in the literature. We revisit the previous computation with the Bethe Ansatz formulation with generic angular momenta and extend it to encompass a large class of competing exponential terms. In the process, we also provide a simplified derivation of the original result. We consider the newly-developed elliptic extension method as well; we apply it to the J 1 ≠ J 2 case, finding a good match with the Bethe Ansatz results. We also investigate the relation between the two different approaches, finding in particular that for every saddle of the elliptic action there are corresponding terms in the Bethe Ansatz formula that match it at large-N.