Non-perturbative Effective Action in Gauge Theories and Quantum Gravity

TL;DR

This paper introduces algebraic methods to compute the non-perturbative low-energy effective action in quantum gravity and gauge theories on curved spaces, summing infinite quantum corrections exactly.

Contribution

It develops a novel algebraic approach to evaluate the heat kernel, enabling exact integral representations of the effective action in curved spacetime.

Findings

Exact integral representation for the effective action

Summation of infinite quantum corrections at low momenta

Generates all terms in the asymptotic expansion without derivatives

Abstract

We use our recently developed algebraic methods for the calculation of the heat kernel on homogeneous bundles over symmetric spaces to evaluate the non-perturbative low-energy effective action in quantum general relativity and Yang-Mills gauge theory in curved space. We obtain an exact integral repesentation for the effective action that generates all terms in the standard asymptotic epxansion of the effective action without derivatives of the curvatures effectively summing up the whole infinite subseries of all quantum corrections with low momenta.