No chiral truncation of quantum log gravity?

TL;DR

This work analyzes the quantum viability of chiral gravity as a left-moving charge truncation of log gravity by studying linearized anti-de Sitter TMG across the chiral point. Using a unitary quantization, the authors show that left-moving Virasoro generators become ill-defined at μ→1, effectively spontaneously breaking the left-moving symmetry and preventing a quantum chiral truncation; the right-moving sector remains intact. In contrast, a non-unitary quantization yields a continuous Hilbert space and well-defined charges at the chiral point, successfully producing a linearized unitary chiral gravity. The results illuminate fundamental issues about defining chiral gravity from TMG/log gravity at the quantum level and suggest intriguing connections and tensions with logarithmic CFT structures and extremal CFT expectations.

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.