No chiral truncation of quantum log gravity?

TL;DR

This paper investigates the quantum properties of chiral gravity and log gravity at the linearized level, revealing that a chiral truncation is not feasible in a unitary quantum framework due to ill-defined left-moving charges.

Contribution

It demonstrates that at the quantum level, chiral truncation fails in a unitary setting because of the ill-defined nature of left-moving Virasoro generators at the chiral point.

Findings

Hilbert space is continuous at the chiral point in TMG

Left-moving Virasoro generators become ill-defined in unitary quantization

Non-unitary quantization allows a consistent chiral gravity theory

Abstract

At the classical level, chiral gravity may be constructed as a consistent truncation of a larger theory called log gravity by requiring that left-moving charges vanish. In turn, log gravity is the limit of topologically massive gravity (TMG) at a special value of the coupling (the chiral point). We study the situation at the level of linearized quantum fields, focussing on a unitary quantization. While the TMG Hilbert space is continuous at the chiral point, the left-moving Virasoro generators become ill-defined and cannot be used to define a chiral truncation. In a sense, the left-moving asymptotic symmetries are spontaneously broken at the chiral point. In contrast, in a non-unitary quantization of TMG, both the Hilbert space and charges are continuous at the chiral point and define a unitary theory of chiral gravity at the linearized level.