On the full asymptotic of analytic torsion

Abstract

The purpose of this article is to study the asymptotic expansion of Ray-Singer analytic tosion associated with increasing powers p of a given positive line bundle. Here we prove that the asymptotic expansion associated to a manifold contains only the terms of the form $p^{n-i}\log p,p^{n-i}$ for $i$-natural. For the two leading terms it was proved by Bismut and Vasserot in 1989. We will calculate the coefficients of the terms $p^{n-1}\log p,p^{n-1}$ in the Kahler case and thus answer the question posed in the recent work of Klevtsov, Ma, Marinescu and Wiegmann about quantuum Hall effect. Our second result concerns the general asymptotic expansion of Ray-Singer analytic torsion for an orbifold.

arXiv commentPublished in Journal of Functional Analysis

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Cited by in corpus (7)

• Analytic torsion for surfaces with cusps I. Compact perturbation theorem and anomaly formula
• The asymptotic of curvature of direct image bundle associated with higher powers of a relatively ample line bundle
• Deligne-Riemann-Roch Theorems I. Uniqueness of Deligne Pairings and Degree $1$ Part of Deligne-Riemann-Roch Isomorphisms
• On full asymptotics of analytic torsions for compact locally symmetric orbifolds
• Geometric Zabrodin-Wiegmann conjecture for integer Quantum Hall states
• The asymptotics of the $L^2$-curvature and the second variation of analytic torsion on Teichmüller space
• The anomaly formula of the analytic torsion on CR manifolds with $S^1$ action