Anomalous Dimensions from Thermal AdS Partition Functions

Understand

We develop an efficient method for computing thermal partition functions of weakly coupled scalar fields in AdS.

• We consider quartic contact interactions and show how to evaluate the relevant two-loop vacuum diagrams without performing any explicit AdS integration, the key step being the use of Kallen-Lehmann type identities.
• This leads to a simple method for extracting double-trace anomalous dimensions in any spacetime dimension, recovering known first-order results in a streamlined fashion.