Index saddle for supersymmetric F1-P black ring

TL;DR

This paper constructs a supersymmetric index saddle for the F1--P black ring, analyzing its properties and potential for matching microscopic results after higher-derivative corrections are considered.

Contribution

It introduces a new supersymmetric index saddle derived from a non-supersymmetric black ring, expressed as a three-center Bena--Warner solution, and discusses its implications.

Findings

The index saddle has a finite-area horizon but a vanishing two-derivative index.

Higher-derivative corrections are expected to produce a finite index value.

Scaling analysis shows agreement with microscopic results up to an undetermined constant.

Abstract

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.