Shape of gauge field tadpoles in string theory

TL;DR

This paper compares field theory and string theory near orbifold singularities, showing string theory smooths out singularities with twisted states and revealing local tachyons in some models.

Contribution

It demonstrates how string theory regularizes orbifold singularities and identifies contributions from twisted states and local tachyons, extending the understanding of gauge field tadpoles.

Findings

String theory contributions spread over a couple of string lengths around singularities.

Field theory is largely confirmed near orbifold fixed points.

Local tachyons can contribute near orbifold fixed points in certain models.

Abstract

Orbifolds in field theory are potentially singular objects for at their fixed points the curvature becomes infinite, therefore one may wonder whether field theory calculations near orbifold singularities can be trusted. String theory is perfectly well defined on orbifolds and can therefore be taken as a UV completion of field theory on orbifolds. We investigate the properties of field and string theory near orbifold singularities by reviewing the computation of a one loop gauge field tadpole. We find that in string theory the twisted states give contributions that have a spread of a couple of string lengths around the singularity, but otherwise the field theory picture is confirmed. One additional surprise is that in some orbifold models one can identify local tachyons that give contributions near the orbifold fixed point.