Stringy profiles of gauge field tadpoles near orbifold singularities: II. field theoretical implications

TL;DR

This paper analyzes string-derived gauge field tadpole profiles near orbifold singularities, showing how string effects smooth out field theory singularities and highlighting the dominance of tachyon effects near fixed points.

Contribution

It provides a detailed comparison of string and field theory profiles of gauge tadpoles, illustrating how string theory avoids delta-function singularities and how tachyons influence local profiles.

Findings

Twisted states are localized within a few string lengths of the singularity.

String effects smooth out field theory delta-like singularities.

Tachyons dominate the tadpole profile near fixed points despite being absent in the spectrum.

Abstract

Recent work has provided a direct string calculation of the internal coordinate dependence of gauge field tadpoles on the orbifold C^3/Z_3. We investigate the structure of these profiles in momentum and coordinate space representations using both analytical and numerical methods. The twisted states are determined to be localized within a few string lengths of the singularity. This provides an example of how delta-like singularities, which are typical for field theories on orbifolds, are avoided in string theory. A systematic expansion of the full string result allows us to speculate on how the leading stringy effects can be incorporated in a field theoretical description. In one heterotic model, we find that even though tachyons are not present in the physical spectrum, they totally dominate the tadpole profile in the vicinity of the fixed point.