Informal Pizza Seminar

One-loop Partition Functions of 3D Gravity

Simone Giombi

Harvard University

Motivated by the problem of pure 3D gravity with a negative cosmological constant, we study one-loop partition functions of quantum fields on locally AdS₃ space-times. We compute explicitly the relevant functional determinants for scalar, vector and graviton excitations by using heat kernel techniques. In the case of thermal AdS, we obtain precisely the result expected from the analysis of Brown and Henneaux: the partition function of 3D gravity includes a sum over boundary excitations which are the Virasoro descendents of the vacuum. Our methods can be also used to obtain the one-loop partition function on more general hyperbolic manifolds with higher genus conformal boundary.