Anomalies and Analytic Torsion on 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 Γ\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.

AMSTeX file, 20 pages

References in corpus (6)

• Zeta-function regularization, the multiplicative anomaly and the Wodzicki residue
• Applications in physics of the multiplicative anomaly formula involving some basic differential operators
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• Product Einstein Manifolds, Zeta-Function Regularization and the Multiplicative Anomaly
• The Conformal Anomaly in General Rank 1 Symmetric Spaces and Associated Operator Product
• Analytic Torsion on Hyperbolic Manifolds and the Semiclassical Approximation for Chern-Simons Theory