Person:

Yin, Xi

In this note we describe the contribution from non-handlebody geometries to the partition function of three-dimensional pure gravity with negative cosmological constant on a Riemann surface of genus greater than one, extending previous considerations for handlebodies.

We consider the one-loop partition function of free quantum field theory in locally Anti-de Sitter space-times. In three dimensions, the one loop determinants for scalar, gauge and graviton excitations are computed explicitly using heat kernel techniques. We obtain precisely the result anticipated by Brown and Henneaux: the partition function includes a sum over "boundary excitations" of AdS3, which are the Virasoro descendants of empty Anti-de Sitter space. This result also allows us to compute the one-loop corrections to the Euclidean action of the BTZ black hole as well its higher genus generalizations.

In this note we study spin chain operators in the (\mathcal{N})=6 Chern-Simons-matter theory recently proposed by Aharony, Bergman, Jafferis and Maldacena to be dual to type IIA string theory in (AdS_4) x (\mathbb{CP}^3). We study the two-loop dilatation operator in the gauge theory, and compare to the Penrose limit on the string theory side.