Exact monopole instantons and cosmological solutions in string theory from abelian dimensional reduction

TL;DR

This paper constructs exact string backgrounds from non-compact coset models, revealing solutions that resemble black holes and cosmological models with specific asymptotic behaviors, using abelian dimensional reduction.

Contribution

It provides explicit string vacuum solutions from $SU(2,1)/SU(2)$ coset models, linking them to known spacetime geometries and cosmological scenarios.

Findings

Derived a five-dimensional singular solution with asymptotic linear dilaton and $S^3$ structure.

Identified a cosmological solution interpolating between a singular phase and an $S^1 imes S^2$ universe.

Reinterpreted solutions as stationary, magnetically charged spacetimes similar to Kerr-Newman.

Abstract

We compute the exact string vacuum backgrounds corresponding to the non-compact coset theory $SU(2,1)/SU(2)$. The conformal field theory defined by the level $k= 4$ results in a five dimensional singular solution that factorizes in an asymptotic region as the linear dilaton solution and a $S^3$ model. It presents two abelian compact isometries that allow to reinterpreting it from a four dimensional point of view as a stationary and magnetically charged space-time resembling in some aspects the Kerr-Newman solution of general relativity. The $k=\frac{13}{7}$ theory on the other hand describes a cosmological solution that interpolates between a singular phase at short times and a $S^1 \times S^2$ universe after some planckian times.