Chiral Scale and Conformal Invariance in 2D Quantum Field Theory

TL;DR

This work studies a chiral, non-Lorentz-invariant 2D QFT with left dilational symmetry and a discrete dilation spectrum, showing that a left local conformal symmetry is automatically present and that right translations are enhanced to either a right-moving Virasoro algebra or a left U(1) Kač-Moody current algebra. The analysis uses Noether currents and canonical commutation relations, exploiting the discreteness of the dilation spectrum to derive a left Virasoro algebra with central charge $c$ (where $c=24\pi O_0$) and, depending on the right-moving charges, either a right Virasoro algebra with central charge $\bar{c}$ or a left Kač-Moody current algebra with level $k$. In the non-minimal case where both $p_-$ and $p_+$ are nonzero, the left and right sectors decouple and form independent algebras. The results provide a structural enhancement principle for chiral 2D scale-invariant QFTs and may have implications for warped AdS$_3$ holography and warped CFTs.

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.