A Superstring Theory in Four Curved Space-Time Dimensions

TL;DR

This paper constructs a novel superstring theory in four curved space-time dimensions using superconformal models, revealing duality properties and singular solutions to Einstein's equations with matter.

Contribution

It introduces an exact N=1 superconformal superstring model in four dimensions based on a gauged WZW model, with new duality features and singular solutions.

Findings

The model exhibits space-time duality similar to R↔1/R in tori.

Provides explicit expressions for metric, dilaton, and Ricci tensor.

Identifies singularities in the curvature scalar as solutions to Einstein's equations.

Abstract

Neveu-Schwarz-Ramond type heterotic and type-II superstrings in four dimensional curved space-time are constructed as exact $N=1$ superconformal theories. The tachyon is eliminated with a GSO projection. The theory is based on the N=1 superconformal gauged WZW model for the anti-de Sitter coset $SO(3,2)/SO(3,1)$ with integer central extension $k=5$. The model has dynamical duality properties in its space-time metric that are similar to the large-small ($R\rightarrow 1/R$) duality of tori. To first order in a $1/k$ expansion we give expressions for the metric, the dilaton, the Ricci tensor and their dual generalizations. The curvature scalar has several singularities at various locations in the 4-dimensional manifold. This provides a new singular solution to Einstein's equations in the presence of matter in four dimensions. A non-trivial path integral measure which we conjectured in previous work for gauged WZW models is verified.