String Threshold corrections from Field Theory

TL;DR

This paper develops a field theory method to compute threshold corrections to gauge couplings in a two-torus compactification, examining the connection with string theory and the impact of winding modes and modular invariance.

Contribution

It introduces a field theory approach to threshold effects, analyzing UV behavior and the role of winding modes, bridging field theory and string theory calculations.

Findings

Field theory can describe UV behavior using momentum modes only.

Winding modes influence threshold corrections and are not captured by pure field theory.

Modular invariance ensures finiteness in heterotic string calculations.

Abstract

A field theory approach to summing threshold effects to the gauge couplings in a two-torus compactification is presented and the link with the (heterotic) string calculation is carefully investigated. We analyse whether the complete UV behaviour of the theory may be described on pure field theory grounds, as due to momentum modes only, and address the role of the winding modes, not included by the field theory approach. ``Non-decoupling'' effects in the low energy limit, due to a small dimension are discussed. The role of modular invariance in ensuring a finite (heterotic) string result is addressed.