Conformal Sigma Models for a Class of $T^{p,q}$ Spaces

TL;DR

This paper constructs a conformal sigma model based on specific coset spaces, resulting in new string backgrounds with metrics of T^{p,q} form, expanding the understanding of non-Einstein conformal backgrounds in string theory.

Contribution

It introduces a conformal sigma model on (G x G')/H coset spaces leading to novel T^{p,q} space backgrounds, including Lorentzian cases, for superstring theory.

Findings

Derived 10D string backgrounds with T^{p,q} metrics.

Established conformal invariance of the sigma models on these cosets.

Connected the models to critical NS-NS superstring backgrounds.

Abstract

We consider a 2-d conformal theory based on (G x G')/ H coset sigma model introduced by Guadagnini, Martellini and Mintchev. It is shown that in the case of {SU(2) x SU(2)}/ U(1) the metric of the corresponding background is of T^{p,q} coset space form (but is not an Einstein one). Similar interpretation is possible for the Lorentzian coset space W_{4,2}= {SL(2,R) x SL(2,R)}/U(1). The resulting 10-d homogeneous space metric on W_{4,2} x T^{p,q} supplemented with 2-form field gives a critical NS-NS superstring background with conformal sigma model interpretation.