Chiral Gravity, Log Gravity and Extremal CFT

TL;DR

This paper investigates chiral gravity and log gravity in AdS3, demonstrating their properties, solutions, and potential dual conformal field theories, including extremal and logarithmic CFTs, with implications for quantum gravity.

Contribution

It establishes the positivity of energy in chiral gravity solutions, characterizes solutions and instabilities, and connects log gravity to logarithmic CFTs, proposing a holographic duality framework.

Findings

Chiral gravity solutions have positive energy and are limited to BTZ black holes.

Log gravity has finite asymptotic charges but is not chiral, containing chiral gravity as a sector.

The Euclidean partition function matches the extremal CFT, supporting a quantum theory of chiral gravity.

Abstract

We show that the linearization of all exact solutions of classical chiral gravity around the AdS3 vacuum have positive energy. Non-chiral and negative-energy solutions of the linearized equations are infrared divergent at second order, and so are removed from the spectrum. In other words, chirality is confined and the equations of motion have linearization instabilities. We prove that the only stationary, axially symmetric solutions of chiral gravity are BTZ black holes, which have positive energy. It is further shown that classical log gravity-- the theory with logarithmically relaxed boundary conditions --has finite asymptotic symmetry generators but is not chiral and hence may be dual at the quantum level to a logarithmic CFT. Moreover we show that log gravity contains chiral gravity within it as a decoupled charge superselection sector. We normally evaluate the Euclidean sum over geometries of chiral gravity and show that it gives precisely the holomorphic extremal CFT partition function. The modular invariance and integrality of the expansion coefficients of this partition function are consistent with the existence of an exact quantum theory of chiral gravity. We argue that the problem of quantizing chiral gravity is the holographic dual of the problem of constructing an extremal CFT, while quantizing log gravity is dual to the problem of constructing a logarithmic extremal CFT.