Moduli Dependence of One--Loop Gauge Couplings in (0,2) Compactifications

TL;DR

This paper derives how one-loop gauge couplings depend on moduli in heterotic (0,2) string compactifications, revealing their representation as modular functions and linking them to the free energy of 2D solitons.

Contribution

It introduces a novel modular function representation of one-loop gauge couplings in heterotic (0,2) models, connecting them to soliton free energies on an auxiliary Riemann surface.

Findings

Gauge couplings depend on moduli through modular functions.

One-loop functions relate to soliton free energy on a Riemann surface.

Representation simplifies understanding of gauge coupling behavior.

Abstract

We derive the moduli dependence of the one--loop gauge couplings for non--vanishing gauge background fields in a four--dimensional heterotic (0,2) string compactification. Remarkably, these functions turn out to have a representation as modular functions on an auxiliary Riemann surface on appropriate truncations of the full moduli space. In particular, a certain kind of one--loop functions is given by the free energy of two--dimensional solitons on this surface.