Gravitational instantons and black plane solutions in 4-d string theory

TL;DR

This paper constructs and analyzes specific four-dimensional string theory backgrounds derived from gauged Wess-Zumino models on non-compact groups, revealing instanton solutions and dualities that connect different cosmological and black plane geometries.

Contribution

It introduces new string vacuum solutions from gauged Wess-Zumino models on SU(2,1), including instantons and dual backgrounds with black plane geometries.

Findings

Identified gravity-dilaton solutions satisfying string equations of motion.

Interpreted solutions as instantons connecting singular universes and black planes.

Computed exact backgrounds and their duals depending on parameter k.

Abstract

We consider gauged Wess-Zumino models based on the non compact group $SU(2,1)$. It is shown that by vector gauging the maximal compact subgroup $U(2)$ the resulting backgrounds obey the gravity-dilaton one loop string vacuum equations of motion in four dimensional euclidean space. The torsionless solution is then interpreted as a pseudo-instanton of the $d=4$ Liouville theory coupled to gravity. The presence of a traslational isometry in the model allows to get another string vacuum backgrounds by using target duality that we identify with those corresponding to the axial gauging. We also compute the exact backgrounds. Depending on the value of $k$, they may be interpreted as instantons connecting a highly singular big bang like universe with a static singular or regular black plane geometry.