Symmetries of Four-dimensional String Effective Action with Cosmological Constant

TL;DR

This paper explores the symmetries of four-dimensional string effective actions with cosmological constants, deriving classical solutions and analyzing how S-duality transformations are affected by the cosmological term.

Contribution

It identifies symmetries of the effective actions and generates new solutions using noncompact transformations, highlighting the impact of the cosmological constant on S-duality.

Findings

Derived classical solutions for Minkowskian and Euclidean cases

Identified symmetries and generated new solutions

Found S-duality is noninvariant due to the cosmological constant

Abstract

Classical solutions for a four-dimensional Minkowskian string effective action and an Euclidean one with cosmological constant term are derived. The former corresponds to electrovac solutions whereas the later solutions are identified as gravitational instanton solutions for Fubini-Study metric. The symmetries of the effective actions are identified and new classical solutions are generated by implementing appropriate noncompact transformations. The S-duality transformations on the equations of motion are discussed and it is found that they are S-duality noninvariant due to the presence of cosmological constant term.