Abstract
We revisit the subject of one-loop determinants in AdS3 gravity via the quasi-normal 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 AdS3 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.
Highlights
One-loop corrections in holography provide a new window into the nature of quantum gravity
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
In AdS3 the one-loop determinant of the graviton very elegantly establishes the anticipated results of Brown & Henneaux [1]: finite energy excitations with Dirichlet boundary conditions fall into representations of the two dimensional conformal group
Summary
One-loop corrections in holography provide a new window into the nature of quantum gravity. The appearance of quasinormal frequencies in the product is directly tied to requiring Dirichlet boundary conditions for each component of the field in question This feature allows us to tweak the DHS method to our agenda: by imposing instead Neumann boundary conditions on certain components of the graviton we will modify the spectrum of frequencies that enter in the functional determinant. This setup in AdS3 is dual to a two dimensional quantum gravity in lightcone gauge, as elegantly argued in [17], and not a conformal theory Since these boundary conditions are chiral (left-moving) in nature, to highlight their features we will need to implement the DHS method for stationary (not static) thermal backgrounds, i.e. for the Euclidean continuation of the rotating BTZ black hole.. Appendix A contains our conventions for the BTZ background, in appendix B we give a detailed study of the spin-2 fluctuations, and in appendix C we describe the ghost spectrum
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