Abstract
We explicitly evaluate the heat kernel for the Laplacian of arbitrary spin tensor fields on the thermal quotient of (Euclidean) AdS N for N ≥ 3 using the group theoretic techniques employed for AdS 3 in arXiv:0911.5085. Our approach is general and can be used, in principle, for other quotients as well as other symmetric spaces.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
J. Polchinski, Evaluation of the One Loop String Path Integral, Commun. Math. Phys. 104 (1986) 37 [inSPIRE].
J.R. David, M.R. Gaberdiel and R. Gopakumar, The Heat Kernel on AdS 3 and its Applications, JHEP 04 (2010) 125 [arXiv:0911.5085] [inSPIRE].
M.R. Gaberdiel, D. Grumiller and D. Vassilevich, Graviton 1-loop partition function for 3-dimensional massive gravity, JHEP 11 (2010) 094 [arXiv:1007.5189] [inSPIRE].
M.R. Gaberdiel, R. Gopakumar and A. Saha, Quantum W-symmetry in AdS 3, JHEP 02 (2011) 004 [arXiv:1009.6087] [inSPIRE].
A. Campoleoni, S. Fredenhagen, S. Pfenninger and S. Theisen, Asymptotic symmetries of three-dimensional gravity coupled to higher-spin fields, JHEP 11 (2010) 007 [arXiv:1008.4744] [inSPIRE].
M. Henneaux and S.-J. Rey, Nonlinear W infinity as Asymptotic Symmetry of Three-Dimensional Higher Spin Anti-de Sitter Gravity, JHEP 12 (2010) 007 [arXiv:1008.4579] [inSPIRE].
M.R. Gaberdiel and R. Gopakumar, An AdS 3 Dual for Minimal Model CFTs, Phys. Rev. D 83 (2011) 066007 [arXiv:1011.2986] [inSPIRE].
C. Fronsdal, Massless Fields with Integer Spin, Phys. Rev. D 18 (1978) 3624 [inSPIRE].
C. Fronsdal, Singletons and Massless, Integral Spin Fields on de Sitter Space (Elementary Particles in a Curved Space. 7., Phys. Rev. D 20 (1979) 848 [inSPIRE].
A. Salam and J. Strathdee, On Kaluza-Klein Theory, Annals Phys. 141 (1982) 316 [inSPIRE].
R. Camporesi, Harmonic analysis and propagators on homogeneous spaces, Phys. Rept. 196 (1990) 1 [inSPIRE].
R. Camporesi and A. Higuchi, On the Eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [inSPIRE].
A.O. Barut and R. Raczka, Theory Of Group Representations And Applications, World Scientific, Singapore (1986).
R. Camporesi and A. Higuchi, On the Eigen functions of the Dirac operator on spheres and real hyperbolic spaces, J. Geom. Phys. 20 (1996) 1 [gr-qc/9505009] [inSPIRE].
W. Fulton and J. Harris, Representation Theory, Springer-Verlag, Heidelberg Germany (1991).
S. Giombi, A. Maloney and X. Yin, One-loop Partition Functions of 3D Gravity, JHEP 08 (2008) 007 [arXiv:0804.1773] [inSPIRE].
S. Helgason, Mathematical Surveys and Monograms. Vol. 83: Groups and geometric analysis: integral geometry, invariant differential operator and spherical function, American Mathematical Society, Providence U.S.A. (2000).
T. Hirai, On irreducible representations of the Lorentz group of n-th order, Proc. Japan Acad. 38 (1962) 258.
U. Ottoson, A classification of the unitary irreducible representations of SO0 (N, 1), Commun. Math. Phys. 8 (1968) 228.
R. Camporesi and A. Higuchi, Spectral functions and zeta functions in hyperbolic spaces, J. Math. Phys. 35 (1994) 4217 [inSPIRE].
T. Hirai, The characters of irreducible representations of the Lorentz group of n-th order, Proc. Japan Acad. 41 (1965) 526.
F. Denef, S.A. Hartnoll and S. Sachdev, Black hole determinants and quasinormal modes, Class. Quant. Grav. 27 (2010) 125001 [arXiv:0908.2657] [inSPIRE].
T. Hartman and L. Rastelli, Double-trace deformations, mixed boundary conditions and functional determinants in AdS/CFT, JHEP 01 (2008) 019 [hep-th/0602106] [inSPIRE].
D.E. Diaz and H. Dorn, Partition functions and double-trace deformations in AdS/CFT, JHEP 05 (2007) 046 [hep-th/0702163] [inSPIRE].
G. Gibbons, M. Perry and C. Pope, Partition functions, the Bekenstein bound and temperature inversion in anti-de Sitter space and its conformal boundary, Phys. Rev. D 74 (2006) 084009 [hep-th/0606186] [inSPIRE].
Author information
Authors and Affiliations
Corresponding author
Additional information
ArXiv ePrint: 1103.3627
Rights and permissions
Open Access This is an open access article distributed under the terms of the Creative Commons Attribution Noncommercial License (https://creativecommons.org/licenses/by-nc/2.0), which permits any noncommercial use, distribution, and reproduction in any medium, provided the original author(s) and source are credited.
About this article
Cite this article
Gopakumar, R., Gupta, R.K. & Lal, S. The heat kernel on AdS. J. High Energ. Phys. 2011, 10 (2011). https://doi.org/10.1007/JHEP11(2011)010
Received:
Revised:
Accepted:
Published:
DOI: https://doi.org/10.1007/JHEP11(2011)010