Borel Summation and Analytic Continuation of the Heat Kernel on Hyperbolic Space

Abstract

The heat kernel expansion on even-dimensional hyperbolic spaces is asymptotic at both short and long times, with interestingly different Borel properties for these short and long time expansions. Resummations in terms of incomplete gamma functions provide accurate extrapolations and analytic continuations, relating the heat kernel to the Schrodinger kernel, and the heat kernel on hyperbolic space to the heat kernel on spheres. For the diagonal heat kernel there is also a duality between short and long times which mixes the scalar and spinor heat kernels.

arXiv comment14 pp, 13 figs; for Festschrift in honor of Peter Suranyi

References in corpus (5)

• The 1/N correction in the D3-brane description of circular Wilson loop at strong coupling
• Resurgence in complex Chern-Simons theory
• Logarithmic Potential Theory with Applications to Approximation Theory
• Uniformization and Constructive Analytic Continuation of Taylor Series
• An introduction to Dunkl theory and its analytic aspects