Chiral Scale and Conformal Invariance in 2D Quantum Field Theory

TL;DR

This paper investigates the emergence of conformal symmetry in two-dimensional quantum field theories with chiral scaling, showing that even with minimal assumptions, conformal structures naturally arise.

Contribution

It demonstrates that in 2D chiral QFTs, a left conformal symmetry always emerges from a global scaling symmetry, and right symmetries are enhanced to either conformal or Kac-Moody symmetries without assuming Lorentz invariance.

Findings

Left conformal symmetry is implied from left scaling symmetry.

Right symmetries are enhanced to conformal or Kac-Moody symmetries.

Lorentz invariance is not assumed in the analysis.

Abstract

It is well known that a local, unitary Poincare-invariant 2D QFT with a global scaling symmetry and a discrete non-negative spectrum of scaling dimensions necessarily has both a left and a right local conformal symmetry. In this paper we consider a chiral situation beginning with only a left global scaling symmetry and do not assume Lorentz invariance. We find that a left conformal symmetry is still implied, while right translations are enhanced either to a right conformal symmetry or a left U(1) Kac-Moody symmetry.