Anomalies and Analytic Torsion on Hyperbolic Manifolds

TL;DR

This paper investigates the properties of Laplacians and zeta functions on hyperbolic manifolds, deriving explicit formulas for analytic torsion and anomalies, enhancing understanding of geometric analysis in hyperbolic spaces.

Contribution

It provides explicit formulas for zeta functions, anomalies, and analytic torsion on hyperbolic manifolds, advancing the mathematical understanding of spectral invariants in these spaces.

Findings

Explicit form of zeta functions on hyperbolic manifolds

Derived multiplicative anomaly formulas

Calculated analytic torsion for connected sums of hyperbolic manifolds

Abstract

The global additive and multiplicative properties of the Laplacian on j-forms and related zeta functions are analyzed. The explicit form of zeta functions on a product of closed oriented hyperbolic manifolds \Gamma\backslash{\Bbb H}^d and of the multiplicative anomaly are derived. We also calculate in an explicit form the analytic torsion associated with a connected sum of such manifolds.