Radiative Contributions to the Effective Action of Self-Interacting Scalar Field on a Manifold with Boundary

TL;DR

This paper investigates quantum corrections to a self-interacting scalar field on a curved manifold with boundary, revealing boundary-induced breaking of conformal invariance and implications for renormalisation.

Contribution

It extends the analysis of quantum effects to manifolds with boundaries using the method of images, showing non-vanishing tadpole contributions and conformal symmetry breaking.

Findings

Boundary contributions break conformal invariance.

Massless tadpole diagrams do not vanish in dimensional regularisation.

Boundary and volume renormalisation are extended in the presence of matter.

Abstract

The effect of quantum corrections to a conformally invariant field theory for a self-interacting scalar field on a curved manifold with boundary is considered. The analysis is most easily performed in a space of constant curvature the boundary of which is characterised by constant extrinsic curvature. An extension of the spherical formulation in the presence of a boundary is attained through use of the method of images. Contrary to the consolidated vanishing effect in maximally symmetric space-times the contribution of the massless "tadpole" diagram no longer vanishes in dimensional regularisation. As a result, conformal invariance is broken due to boundary-related vacuum contributions. The evaluation of one-loop contributions to the two-point function suggests an extension, in the presence of matter couplings, of the simultaneous volume and boundary renormalisation in the effective action.