Instantons from Low Energy String Actions

TL;DR

This paper investigates instanton solutions within low energy string-inspired gravity models, identifying conditions for non-singular instantons and analyzing the behavior of singular solutions, contributing to understanding quantum effects in string cosmology.

Contribution

It introduces specific conditions under which non-singular instantons exist in low energy string actions with scalar fields and potentials.

Findings

Non-singular instantons exist if the Dilaton potential has a minimum.

Singular instantons may have finite action depending on parameter values.

The volume factor's behavior at singularities affects the finiteness of the instanton action.

Abstract

We look for instanton solutions in a class of two scalar field gravity models, which includes the low energy string action in four dimensions. In models where the matter field has a potential with a false vacuum, we find that non-singular instantons exist as long as the Dilaton field found in string theory has a potential with a minimum, and provide an example of such an instanton. The class of singular instanton solutions are also examined, and we find that depending on the parameter values, the volume factor of the Euclidean region does not always vanish fast enough at the singularity to make the action finite.