Nonperturbative heat kernel and nonlocal effective action

TL;DR

This paper reviews recent nonperturbative results on the heat kernel and its late time behavior, deriving a generalized nonlocal effective action that extends the Coleman-Weinberg potential to non-homogeneous fields and curved spacetimes.

Contribution

It introduces a new nonlocal, nonperturbative effective action for massless theories, generalizing the Coleman-Weinberg potential to non-homogeneous and curved spacetime scenarios.

Findings

Derived a nonlocal generalization of the Coleman-Weinberg potential.

Analyzed nonperturbative heat kernel behavior in curved, asymptotically-flat spacetime.

Identified effects of nonlocality on the infrared structure of quantum effective action.

Abstract

We present an overview of recent nonperturbative results in the theory of heat kernel and its late time asymptotics responsible for the infrared behavior of quantum effective action for massless theories. In particular, we derive the generalization of the Coleman-Weinberg potential to physical situations when the field is not homogeneous throughout the whole spacetime. This generalization represents a new nonlocal and nonperturbative action accounting for the effects of a transition domain between the spacetime interior and its infinity. In four dimensions these effects delocalize the logarithmic Coleman-Weinberg potential, while in $d>4$ they are dominated by new powerlike and renormalization-independent nonlocal structure. Nonperturbative behavior of the heat kernel is also constructed in curved spacetime with asymptotically-flat geometry, and its conformal properties are analyzed for conformally invariant scalar field. The problem of disentangling the local cosmological term from nonlocal effective action is discussed.