Extreme Domain Wall--Black Hole Complementarity in N=1SUPERGRAVITY with a General Dilaton Coupling

TL;DR

This paper investigates supersymmetric domain walls in 4D N=1 supergravity with a general dilaton coupling, revealing a classification based on the coupling value and its relation to black hole solutions.

Contribution

It provides a classification of supersymmetric domain walls in N=1 supergravity with arbitrary dilaton coupling and links their global structure to magnetically charged black holes.

Findings

For $ ext{alpha} = 1$, the theory models effective superstring theory.

The global space-time structure depends on whether $ ext{alpha} > 1$ or $ ext{alpha} < 1$.

The space-time of domain walls with coupling $ ext{alpha}$ matches that of black holes with coupling $1/ ext{alpha}$.

Abstract

We study supersymmetric (extreme) domain walls in four-dimensional (4d) N=1 supergravity theories with a general dilaton coupling $\alpha > 0$. Type I walls, which are static, planar (say, in ($x,y$) plane) configurations, interpolate between Minkowski space-time and a vacuum with a varying dilaton field. We classify their global space-time with respect to the value of the coupling $\alpha$. $N=1$ supergravity with $\alpha =1$, an effective theory from superstrings, provides a dividing line between the theories with $\alpha>1$, where there is a naked (planar) singularity on one side of the wall, and the theories with $\alpha<1$, where the singularity of the of the wall is covered by the horizon. The global space-time (in $(t,z$) direction) of the extreme walls with the coupling $\alpha$ is the same as the global space-time (in ($t,r)$ direction) of the extreme magnetically charged black holes with the coupling $1/\alpha$.