On the effective action for scalars in a general manifold to any loop order

TL;DR

This paper develops a covariant functional method to compute the effective action for scalar fields on arbitrary manifolds to any loop order, with applications in effective field theories and electroweak symmetry breaking.

Contribution

It introduces a geometric, covariant approach to calculate the effective action at all loop orders for scalars on general manifolds, extending previous one-loop results.

Findings

Provides a systematic procedure for multi-loop effective actions

Maintains explicit field-space covariance throughout the calculations

Extends geometric methods beyond one-loop order

Abstract

Functional methods and a derivative expansion are employed for laying out a procedure to compute the effective action to any loop order, for scalar fields parametrising an arbitrary Riemannian manifold, while maintaining explicit field-space covariance. In this process, the geometric generalization of the LSZ reduction formula is presented. These results are of use in the characterization of effective field theories for electroweak symmetry breaking and extend a geometric perspective in field space beyond one loop.