Article

Journal of High Energy Physics

, 2010:125

The heat kernel on AdS 3 and its applications

  • Justin R. DavidAffiliated withCentre for High Energy Physics, Indian Institute of Science Email author 
  • , Matthias R. GaberdielAffiliated withInstitut für Theoretische Physik, ETH Zurich
  • , Rajesh GopakumarAffiliated withHarish-Chandra Research Institute

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Abstract

We derive the heat kernel for arbitrary tensor fields on S 3 and (Euclidean) AdS3 using a group theoretic approach. We use these results to also obtain the heat kernel on certain quotients of these spaces. In particular, we give a simple, explicit expression for the one loop determinant for a field of arbitrary spin s in thermal AdS3. We apply this to the calculation of the one loop partition function of \( \mathcal{N} = 1 \) supergravity on AdS3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the \( {\text{SL}}\left( {2,\mathbb{C}} \right) \) invariant vacuum, as argued by Maloney and Witten on general grounds.

Keywords

AdS-CFT Correspondence Classical Theories of Gravity Supergravity Models