Criteria for Conformal Invariance of (0,2) Models

TL;DR

This paper discusses conditions under which (0,2) models in string theory become conformally invariant in the infrared, analyzing the effective superpotential through variations in Kahler class and complex structure.

Contribution

It introduces criteria for conformal invariance of (0,2) models by analyzing superpotential behavior via Kahler and complex structure variations.

Findings

Superpotential must vanish due to absence of poles.

Yukawa couplings exhibit simple poles in certain cases.

World-sheet instanton sum does not detect gauge bundle singularities.

Abstract

It is argued that many linear (0,2) models flow in the infrared to conformally invariant solutions of string theory. The strategy in the argument is to show that the effective space-time superpotential must vanish because there is no place where it can have a pole. This conclusion comes from either of two different analyses, in which the Kahler class or the complex structure of the gauge bundle is varied, while keeping everything else fixed. In the former case, we recover from the linear sigma model the usual simple pole in the ${\bf \bar {27}}^3$ Yukawa coupling but show that an analogous pole does not arise in the couplings of gauge singlet modes. In the latter case, a dimension count shows that the world-sheet instanton sum does not ``see'' the singularities of the gauge bundle and hence cannot have a pole.