The heat kernel on AdS3 and its applications

  • Justin R. David
  • Matthias R. Gaberdiel
  • Rajesh Gopakumar


We derive the heat kernel for arbitrary tensor fields on S3 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.


AdS-CFT Correspondence Classical Theories of Gravity Supergravity Models 


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Copyright information

© SISSA, Trieste, Italy 2010

Authors and Affiliations

  • Justin R. David
    • 1
  • Matthias R. Gaberdiel
    • 2
  • Rajesh Gopakumar
    • 3
  1. 1.Centre for High Energy PhysicsIndian Institute of ScienceBangaloreIndia
  2. 2.Institut für Theoretische PhysikETH ZurichZürichSwitzerland
  3. 3.Harish-Chandra Research InstituteJhusiIndia

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