Tweaking one-loop determinants in AdS$_3$

TL;DR

This paper refines the calculation of one-loop determinants in AdS$_3$ gravity with chiral boundary conditions, extending the quasinormal mode method to stationary backgrounds and confirming results with dual warped CFT predictions.

Contribution

It generalizes the quasinormal mode method for stationary backgrounds and introduces a new approach for Neumann boundary conditions in AdS$_3$ gravity.

Findings

Computed graviton one-loop determinant on Euclidean BTZ background with parity-violating boundary conditions.

Found excellent agreement with dual warped CFT predictions.

Discussed novel ghost field behavior under different boundary conditions.

Abstract

We revisit the subject of one-loop determinants in AdS$_3$ gravity via the quasinormal mode method. Our goal is to evaluate a one-loop determinant with chiral boundary conditions for the metric field; chirality is achieved by imposing Dirichlet boundary conditions on certain components while others satisfy Neumann. Along the way, we give a generalization of the quasinormal mode method for stationary (non-static) thermal backgrounds, and propose a treatment for Neumann boundary conditions in this framework. We evaluate the graviton one-loop determinant on the Euclidean BTZ background with parity-violating boundary conditions (CSS), and find excellent agreement with the dual warped CFT. We also discuss a more general falloff in AdS$_3$ that is related to two dimensional quantum gravity in lightcone gauge. The behavior of the ghost fields under both sets of boundary conditions is novel and we discuss potential interpretations.