Abstract
We derive the heat kernel for arbitrary tensor fields on S^3 and (Euclidean) AdS_3 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 AdS_3. We apply this to the calculation of the one loop partition function of N=1 supergravity on AdS_3. We find that the answer factorizes into left- and right-moving super Virasoro characters built on the SL(2, C) invariant vacuum, as argued by Maloney and Witten on general grounds.
Highlights
In studying the quantization of field theories on a general spacetime an important tool which captures the leading quantum properties of the theory is the heat kernel of the Laplacian
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 N = 1 supergravity on AdS3
Knowing the heat kernel enables one to compute, for instance, the one loop determinants that contribute to the free energy
Summary
The fields of arbitrary spin s are sections of what are known as homogeneous vector bundles on these coset spaces This will allow us to use some well-known techniques of harmonic analysis to write down the eigenfunctions of the. We check that this answer correctly reproduces all the previously known cases (i.e. spins s = 0, 1, 2).
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