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The heat kernel on AdS 3 and its applications

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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.

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Authors and Affiliations

  1. Centre for High Energy Physics, Indian Institute of Science, Bangalore, 560012, India

    Justin R. David

  2. Institut für Theoretische Physik, ETH Zurich, CH-8093, Zürich, Switzerland

    Matthias R. Gaberdiel

  3. Harish-Chandra Research Institute, Chhatnag Road, 211019, Jhusi, India

    Rajesh Gopakumar

Authors
  1. Justin R. David
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  2. Matthias R. Gaberdiel
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  3. Rajesh Gopakumar
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Correspondence to Justin R. David.

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ArXiv ePrint: 0911.5085

On leave from Harish-Chandra Research Institute, Allahabad. (Justin R. David)

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David, J.R., Gaberdiel, M.R. & Gopakumar, R. The heat kernel on AdS 3 and its applications. J. High Energ. Phys. 2010, 125 (2010). https://doi.org/10.1007/JHEP04(2010)125

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  • DOI: https://doi.org/10.1007/JHEP04(2010)125

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