Supersymmetric black rings and non-linear sigma models

TL;DR

This paper explores the use of a non-linear sigma model derived from five-dimensional supergravity to analyze supersymmetric black ring solutions, providing new insights into their algebraic structure and quantum properties.

Contribution

It applies a specific sigma model to supersymmetric black rings, deriving their algebra of conserved charges, supersymmetry constraints, and semi-classical wave function, advancing understanding of these solutions.

Findings

Derived a two-dimensional Lagrangian for black rings

Analyzed the algebra of conserved charges and supersymmetry constraints

Obtained the semi-classical wave function of supersymmetric black rings

Abstract

In this paper we investigate the non-linear sigma model arising in the reduction of D = 5 supergravity to D = 3, and present the application of this sigma model to supersymmetric black ring solutions in five-dimensional minimal supergravity. With the ansatz of stationary solutions with $R \times U(1)\times U(1)$ isometry, we obtain a two-dimensional Lagrangian corresponding to geodesic motion of a string-like object on the coset $G_{2(+2)}/SO(4)$, and study the algebra of conserved charges and supersymmetry constraints of supersymmetric black rings. We also obtain the semi-classical wave function of supersymmetric black rings.