Per Kraus

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.

Virasoro conformal blocks are expected to exponentiate in the limit of large central charge c and large operator dimensions h _i , with the ratios h _i /c held fixed. We prove this by employing the oscillator formulation of the Virasoro algebra and its representations. The techniques developed are then used to provide new derivations of some standard results on conformal blocks.

The blackbody theory of Planck played a seminal role in the development of quantum theory at the turn of the past century. A blackbody cavity is generally thought to be a collection of photons in thermal equilibrium; the radiation emitted is at all wavelengths, and the intensity follows a scaling law, which is Planck's characteristic distribution law. These photons arise from non-interacting normal modes. Here we suggest that certain quantum critical states when heated emit "radiation" at all wavelengths and satisfy all the criteria of a blackbody. An important difference is that the "radiation" does not necessarily consist of non-interacting photons, but also emergent relativistic bosons or fermions. The examples we provide include emergent relativistic fermions at a topological quantum critical point. This perspective on a quantum critical state may be illuminating in many unforeseen ways.