One-loop partition function, gauge accessibility and spectra in AdS3 gravity

A bstract We continue the study of one-loop partition function AdS 3 gravity with focus on square-integrability condition fluctuating fields. In a previous work we found that Brown-Henneaux boundary conditions follow directly from L 2 condition. Here rederive as ratio Laplacian determinants by performing suitable decomposition metric fluctuations. pay special attention to asymptotics fields appearing in function. also show usual computation using ghost for de Donder gauge, such gauge is accessible precisely square-integrable Finally, compute spectrum relevant Laplacians thermal , particular noticing there are no isolated eigenvalues, only essential spectrum. This last result supports analytic continuation approach David, Gaberdiel and Gopakumar. The purely spectra consistent independent results Lee Delay TT rank-2 tensor Lichnerowickz asymptotically hyperbolic spaces.