Heat kernel coefficients on the sphere in any dimension

Abstract

We derive all heat kernel coefficients for Laplacians acting on scalars, vectors, and tensors on fully symmetric spaces, in any dimension. Final expressions are easy to evaluate and implement, and confirmed independently using spectral sums and the Euler-Maclaurin formula. We also obtain the Green's function for Laplacians acting on transverse traceless tensors in any dimension, and new integral representations for heat kernels using known eigenvalue spectra of Laplacians. Applications to quantum gravity and the functional renormalisation group, and other, are indicated.

arXiv comment33 pages, v2: results on spectral integrals and analytic continuation added; matches with published version

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Cited by in corpus (8)

• The nonperturbative functional renormalization group and its applications
• Beta functions of (3+1)-dimensional projectable Horava gravity
• Fixed Points of Quantum Gravity and the Dimensionality of the UV Critical Surface
• Functional Renormalisation for $f(R_{\mu \nu \rho \sigma })$ Quantum Gravity
• New Heat Kernel Method in Lifshitz Theories
• Heat kernel coefficients for massive gravity
• Gravitons on Nariai Edges
• Running of the Number of Degrees of Freedom in Quantum Conformal Gravity