The Worldvolume Action of Kink Solitons in AdS Spacetime

TL;DR

This paper develops a formalism to compute higher-order corrections to the worldvolume action of kink solitons in AdS spacetime, revealing new interactions and extending applicability to conformally flat backgrounds.

Contribution

It introduces a method for calculating corrections to kink worldvolume actions in AdS, including non-Galileon terms, and extends to conformally flat spacetimes.

Findings

Explicit kink solutions in AdS spacetime.

Quadratic order corrections involving extrinsic and intrinsic curvatures.

Identification of non-Galileon terms in the worldvolume action.

Abstract

A formalism is presented for computing the higher-order corrections to the worldvolume action of co-dimension one solitons. By modifying its potential, an explicit "kink" solution of a real scalar field in AdS spacetime is found. The formalism is then applied to explicitly compute the kink worldvolume action to quadratic order in two expansion parameters--associated with the hypersurface fluctuation length and the radius of AdS spacetime respectively. Two alternative methods are given for doing this. The results are expressed in terms of the trace of the extrinsic curvature and the intrinsic scalar curvature. In addition to conformal Galileon interactions, we find a non-Galileon term which is never sub-dominant. This method can be extended to any conformally flat bulk spacetime.