Global U(1) R-Symmetry And Conformal Invariance Of (0,2) Models

TL;DR

This paper establishes conditions for (0,2) linear sigma models to have a conformal stress tensor in $q$ cohomology, linking classical quasihomogeneity to quantum anomaly cancellation for a specific U(1) R-symmetry.

Contribution

It derives a criterion connecting classical superpotential quasihomogeneity with quantum anomaly cancellation in (0,2) models, ensuring conformal invariance.

Findings

Classical quasihomogeneity enforces a conformal stress tensor at the classical level.

Quantum anomaly cancellation conditions are equivalent to R-symmetry charge and superpotential degree constraints.

The structure persists at the quantum level only if specific charge and degree conditions are satisfied.

Abstract

We derive a condition under which (0,2) linear sigma models possess a ``left-moving'' conformal stress tensor in $\bq$ cohomology (i.e. which leaves invariant the ``right-moving'' ground states) even away from their critical points. At the classical level this enforces quasihomogeneity of the superpotential terms. The persistence of this structure at the quantum level on the worldsheet is obstructed by an anomaly unless the charges and superpotential degrees satisfy a condition which is equivalent to the condition for the cancellation of the anomaly in a particular ``right-moving'' U(1) R-symmetry.