Stable Singularities in String Theory

TL;DR

This paper investigates a topological obstruction in string theory related to deforming singular target spaces, revealing that certain geometric smoothings are incompatible with conformal field theory consistency due to torsion effects.

Contribution

It identifies a novel topological obstruction in string theory caused by torsion in the target space homology, connecting geometric deformations with conformal field theory anomalies.

Findings

Deformations of singular target spaces can be obstructed by torsion effects.

Discontinuous changes in correlation functions indicate fundamental obstructions.

Links between geometric obstructions and orbifolds with discrete torsion are established.

Abstract

We study a topological obstruction of a very stringy nature concerned with deforming the target space of an $N=2$ non-linear \sm. This target space has a singularity which may be smoothed away according to the conventional rules of geometry but when one studies the associated conformal field theory one sees that such a deformation is not possible without a discontinuous change in some of the correlation functions. This obstruction appears to come from torsion in the homology of the target space (which is seen by deforming the theory by an irrelevant operator). We discuss the link between this phenomenon and orbifolds with discrete torsion as studied by Vafa and Witten.