The Effective Action and Geometry of Closed N=2 Strings

TL;DR

This paper analyzes the effective action of scalars in N=2 closed strings, revealing that the eta-string's scalar relates to self-dual gravity, while the alpha-string's scalar describes a self-dual curvature with torsion.

Contribution

It computes the effective action of the scalar in the alpha-string, showing it as a deformation of a potential governing metric, torsion, and dilaton, expanding understanding of N=2 string dynamics.

Findings

The eta-string scalar is a deformation of the Kähler potential and relates to self-dual gravity.

The alpha-string scalar is a deformation of a potential determining metric, torsion, and dilaton.

The alpha-string scalar describes a self-dual curvature with torsion.

Abstract

N=2 closed strings have been recently divided in hep-th/0211147 to two T-dual families denoted by \alpha and \beta. In (2,2) signature both families have one scalar in the spectrum. The scalar in the \beta-string is known to be a deformation of the target space K\"ahler potential and the dynamics is that of self-dual gravity. In this paper we compute the effective action of the scalar in the \alpha-string. The scalar is a deformation of a potential that determines the metric, torsion and dilaton. The scalar is free and the dynamics is that of a self-dual curvature with torsion.