Dimensional regularization of nonlinear sigma models on a finite time interval

TL;DR

This paper extends dimensional regularization to nonlinear sigma models on finite intervals, requiring only a covariant two-loop counterterm, simplifying previous regularization approaches in quantum mechanical path integrals in curved space.

Contribution

It introduces a covariant dimensional regularization scheme for nonlinear sigma models on finite intervals, reducing the complexity of counterterms needed.

Findings

Dimensional regularization on finite intervals requires only a R/8 counterterm.

The scheme is covariant and simplifies previous regularization methods.

It advances the understanding of quantum mechanical path integrals in curved space.

Abstract

We extend dimensional regularization to the case of compact spaces. Contrary to previous regularization schemes employed for nonlinear sigma models on a finite time interval (``quantum mechanical path integrals in curved space'') dimensional regularization requires only a covariant finite two-loop counterterm. This counterterm is nonvanishing and given by R/8.