On a class of finite sigma-models and string vacua; a supersymmetric extension

TL;DR

This paper explores a supersymmetric extension of sigma-models in string theory, demonstrating that the metric remains exactly known due to the beta function's reduction to one-loop, confirming Tseytlin's conjecture.

Contribution

It introduces a supersymmetric extension of finite sigma-models with symmetric homogeneous Kähler target spaces, confirming the exactness of the metric via beta function analysis.

Findings

The beta function reduces to its one-loop value for the supersymmetric model.

The metric of the sigma-model is exactly determined.

The results support Tseytlin's conjecture on the supersymmetric extension.

Abstract

Following a suggestion made by Tseytlin, we investigate the case when one replaces the transverse part of the bosonic action by an $n=2$ supersymmetric sigma-model with a symmetric homogeneous K\"ahlerian target space. As conjectured by Tseytlin, the metric is shown to be exactly known since the beta function is known to reduce to its one-loop value.