The Schwinger-DeWitt technique for quantum effective action in brane induced gravity models

TL;DR

This paper develops a covariant curvature expansion technique for quantum effective actions in brane induced gravity models, revealing a higher cutoff scale than previously known and calculating leading orders for scalar fields in curved spacetime.

Contribution

It introduces the Schwinger-DeWitt technique for covariant curvature expansion in brane gravity models, providing new insights into cutoff scales and ultraviolet divergences.

Findings

Cutoff scale is the geometric average of bulk field mass and DGP scale.

Lowest order curvature expansion calculated for scalar fields in curved spacetime.

Ultraviolet divergences identified for four-dimensional branes.

Abstract

We develop the Schwinger-DeWitt technique for the covariant curvature expansion of the quantum effective action for brane induced gravity models in curved spacetime. This expansion has a part nonanalytic in DGP type scale parameter, leading to the cutoff scale which is given by the geometric average of the mass of the quantum field in the bulk and DGP scale. This cutoff is much higher than the analogous strong coupling scale of the DGP model treated by weak field expansion in the tree-level approximation. The lowest orders of this curvature expansion are calculated for the case of the scalar field in the $(d+1)$-dimensional bulk with the brane carrying the $d$-dimensional kinetic term of this field. The ultraviolet divergences in this model are obtained for a particular case of $d=4$.