Amitabh Virmani

A bstract: Boruch, Emparan, Iliesiu, and Murthy recently discussed index saddles for 5D black strings, showing that the black string saddle admits a decoupling limit to a complex, finite-temperature BTZ × S ² saddle that computes the index of the dual CFT. In this paper, we pursue an analogous construction for the D1-D5-P black string. We construct a four-charge index saddle in the four-dimensional STU model as the BPS limit of the non-extremal four-charge black hole, and show that it exhibits the new form of attraction. We then uplift it successively to five and six dimensions, via the 4D-5D connection and a chain of string dualities, to obtain the gravitational index saddle for the D1-D5-P black string. We take a systematic decoupling limit of this index saddle and obtain the BTZ × S ³ saddle that computes the index of the D1-D5 CFT.

A bstract: We construct singly and doubly spinning non-supersymmetric F1–P black ring solutions in five-dimensional supergravity. These black rings have regular horizons and non-zero temperature. The singly spinning configuration lies in the duality orbit of the black ring constructed by Elvang, Emparan, and Figueras, while the doubly spinning configuration is a charged extension of the black ring constructed by Chen, Hong, and Teo. We analyze the physical properties of these solutions and the various limits they admit. In particular, the doubly spinning solution admits an extremal limit in which the entropy satisfies the relation S = 2 πJ _ϕ , thereby linking it directly to the angular momentum on the S ² .

A bstract: We construct the index saddle for the supersymmetric F1-P black ring. Our construction proceeds by taking a supersymmetric limit of a non-supersymmetric doubly spinning F1-P black ring. We express the resulting saddle as a three-center Bena-Warner solution. The black ring saddle possesses a finite-area event horizon, yet the two-derivative index vanishes. The solution is singular on certain subspaces of the horizon, where higher-derivative corrections are expected to become important. We argue that, once such corrections are taken into account, the solution can yield a finite result. In particular, we present a scaling analysis showing that the index agrees with the microscopic result, up to an overall numerical constant that cannot be fixed by the scaling argument alone. This analysis applies only within a restricted region of parameter space, whose full significance is not yet fully understood.

We construct the index saddle for the supersymmetric F1--P black ring. Our construction proceeds by taking a supersymmetric limit of a non-supersymmetric doubly spinning F1--P black ring. We express the resulting saddle as a three-center Bena--Warner solution. The black ring saddle possesses a finite-area event horizon, yet the two-derivative index vanishes. The solution is singular on certain subspaces of the horizon, where higher-derivative corrections are expected to become important. We argue that, once such corrections are taken into account, the solution can yield a finite result. In particular, we present a scaling analysis showing that the index agrees with the microscopic result, up to an overall numerical constant that cannot be fixed by the scaling argument alone. This analysis applies only within a restricted region of parameter space, whose full significance is not yet fully understood.

A bstract: Certain supersymmetric elementary string states with angular momentum can be viewed as small black rings in a five-dimensional string theory. These black rings have zero area event horizon. The 4D-5D connection relates these small rings to small black holes without angular momentum in one less dimension. Recent works have proposed saddle solutions that compute the supersymmetric index for small black holes using gravitational path integral. In this paper, we propose an analogous saddle solution for a five-dimensional small black ring. The dominant contribution comes from a black ring saddle that rotates in both independent planes in five dimensions and has a finite area event horizon. We also write the saddle solution as a three center Bena-Warner solution.

Certain supersymmetric elementary string states with angular momentum can be viewed as small black rings in a five-dimensional string theory. These black rings have zero area event horizon. The 4D-5D connection relates these small rings to small black holes without angular momentum in one less dimension. Recent works have proposed saddle solutions that compute the supersymmetric index for small black holes using gravitational path integral. In this paper, we propose an analogous saddle solution for a five-dimensional small black ring. The dominant contribution comes from a black ring saddle that rotates in both independent planes in five dimensions and has a finite area event horizon. We also write the saddle solution as a three-center Bena-Warner solution.

In a recent paper, Anupam, Chowdhury, and Sen [arXiv:2308.00038] constructed the non-extremal saddle that reproduces the supersymmetric index of the BMPV black hole with three independent charges in the classical limit. This saddle solution is a finite temperature complex solution saturating the BPS bound. In this paper, we write this solution in a canonical form in terms of harmonic functions on three-dimensional flat base space, thereby showing that it is supersymmetric. We also show that it exhibits the new form of attraction.

We compute the supersymmetric index of half BPS black holes in N=2 supergravity with higher curvature corrections and show that the result agrees with the degeneracy of supersymmetric extremal black holes carrying the same charges. Both sides of the computation are done gravitationally.