Supersymmetric Asymptotic AdS and Lifshitz Solutions in Einstein-Weyl and Conformal Supergravities

TL;DR

This paper explores supersymmetric Lifshitz and AdS vacua in Einstein-Weyl supergravity, providing exact solutions, black hole examples, and analyzing their properties, including stability, singularities, and symmetry features.

Contribution

It introduces new supersymmetric Lifshitz solutions in Einstein-Weyl supergravity and analyzes their properties, including black hole solutions and their geometric features.

Findings

Existence of supersymmetric Lifshitz vacua with specific exponents

Construction of extremal AdS and Lifshitz black holes

Identification of smooth wormhole solutions and singular black holes

Abstract

We show that there exist supersymmetric Lifshitz vacua in off-shell Einstein-Weyl supergravity, in addition to the BPS AdS_4 vacuum. The Lifshitz exponents are determined by the product of the cosmological constant and the coupling of the Weyl-squared term. We then obtain the equations of the supersymmetric solutions that are asymptotic to the AdS or Lifshitz vacua. We obtain many examples of exact solutions as well as numerical ones. We find examples of extremal AdS black branes whose near-horizon geometry is AdS_2\times T^2. We also find an extremal Lifshitz black hole with z=-2, whose horizon coincides with the curvature singularity. However the asymptotic Lifshitz solutions are in general smooth wormholes. In conformal supergravity, we find intriguing examples of non-extremal "BPS" AdS and Lifshitz black holes whose local Killing spinor is divergent on the horizon. We show that all the supersymmetric asymptotic AdS and Lifshitz solutions have the vanishing Noether charge associated with some scaling symmetry. We also study the integrability condition of the Killing spinor equation and the supersymmetric invariance of the action. Finally we show that the only spherically-symmetric BPS solution is the AdS vacuum.