(0,2) Heterotic Gauge Couplings and their M-Theory Origin

TL;DR

This paper explores the mathematical structure of gauge couplings in heterotic string theories compactified on K3 x T^2 and relates them to automorphic forms, comparing with M-theory compactifications.

Contribution

It establishes a connection between automorphic forms on SO(s+2,2) and one-loop gauge corrections in heterotic string compactifications, extending to orbifold limits and M-theory.

Findings

Gauge corrections expressed via automorphic forms and instanton numbers.

Automorphic forms classify one-loop gauge thresholds in heterotic orbifold compactifications.

Comparison with M-theory compactifications confirms the consistency of the automorphic form approach.

Abstract

We work out the relation between automorphic forms on SO(s+2,2) and gauge one-loop corrections of heterotic K3 x T^2 string compactifications for the cases s=0,1. We find that one-loop gauge corrections of any orbifold limit of K3 can always be expressed by their instanton numbers and generic automorphic forms.These functions classify also one-loop gauge thresholds of N=1 (0,2) heterotic compactifications based on toroidal orbifolds T^6/Z_N. We compare these results with the gauge couplings of M-theory compactified on S^1/Z_2 x T^6/Z_N using Witten's Calabi-Yau strong coupling expansion.