Supersymmetry of Black Strings in D=5 Gauged Supergravities

TL;DR

This work constructs and analyzes supersymmetric magnetic string solutions in gauged D=5, N=2 supergravity with abelian vector multiplets. It identifies a magnetically charged black string with hyperbolic transverse geometry that preserves 1/4 of the supersymmetry and exhibits near-horizon enhancement to $AdS_3\times H^2$, akin to ungauged theories. The study of general product-space compactifications shows that hyperbolic internal spaces are required to preserve any supersymmetry, with BTZ$_{\rm ext}\times H^2 yielding 1/4$ SUSY; the results have implications for AdS/CFT and potential microstate counting in related backgrounds. The authors also discuss uplifts to ten dimensions and holographic interpretations in the dual CFT on $\mathbb{R}^2\times H^2$.

Abstract

Supersymmetry of five dimensional string solutions is examined in the context of gauged D=5, N=2 supergravity coupled to abelian vector multiplets. We find magnetic black strings preserving one quarter of supersymmetry and approaching the half-supersymmetric product space AdS_3\times H^2 near the event horizon. The solutions thus exhibit the phenomenon of supersymmetry enhancement near the horizon, like in the cases of ungauged supergravity theories, where the near horizon limit is fully supersymmetric. Finally, product space compactifications are studied in detail, and it is shown that only for negative curvature (hyperbolic) internal spaces, some amount of supersymmetry can be preserved. Among other solutions, we find that the extremal rotating BTZ black hole tensored by H^2 preserves one quarter of supersymmetry.