Higher Order Couplings from Heterotic Orbifold Theory

TL;DR

This paper computes higher order couplings in heterotic orbifold string theory using conformal field theory, providing a general rule for instanton corrections and analyzing both classical and quantum contributions.

Contribution

It introduces a comprehensive method to calculate arbitrary order couplings from twisted strings, extending the area rule to non-polygonal configurations and including linearly combined states.

Findings

Derived explicit classical and quantum amplitudes for twisted string couplings.

Generalized the area rule for instanton contributions beyond polygonal configurations.

Provided formulas involving gamma functions for quantum corrections.

Abstract

We calculate couplings of arbitrary order from correlation functions among twisted strings, using conformal field theory. Twisted strings arise in heterotic string compactified on orbifolds yielding matter fields in the low energy limit. We calculate completely the classical and the quantum amplitude including normalization, up to a contribution from Kahler potential. The classical action has saddle points which are interpreted as worldsheet instantons described by metastable untwisted strings, formed by twisted strings distributed at certain fixed points. This understanding generalizes the area rule, in the case that the locations of twisted strings do not form a polygon, and provides a general rule for calculating these kinds of instanton corrections. An interpretation of couplings involving linearly combined states is given, which commonly appear in non-prime order orbifolds. The quantum part of the amplitude is given by ratios of gamma functions with order one arguments.