One-loop effective potential on hyperbolic manifolds

TL;DR

This paper investigates the one-loop effective potential for scalar fields on compact hyperbolic manifolds using zeta-function regularization, exploring renormalization, symmetry breaking, and topological mass generation.

Contribution

It provides a detailed analysis of the effective potential on hyperbolic manifolds and discusses regularization methods, renormalization group equations, and physical phenomena like symmetry breaking.

Findings

Derived renormalization group equations for hyperbolic manifolds

Analyzed the connection between conformal anomaly and effective potential

Discussed mechanisms of symmetry breaking and topological mass generation

Abstract

The one-loop effective potential for a scalar field defined on an ultrastatic space-time whose spatial part is a compact hyperbolic manifold, is studied using zeta-function regularization for the one-loop effective action. Other possible regularizations are discussed in detail. The renormalization group equations are derived and their connection with the conformal anomaly is pointed out. The symmetry breaking and the topological mass generation are also discussed.