Domain walls and torsion potentials

Abstract

A Lagrangian for flat domain walls in spaces with Cartan torsion and electromagnetic fields is proposed.The Lagrangian is very similar to a recently proposed Lagrangian for domain walls in a Chern-Simons electrodynamics in 2+1 dimensions.We show that in the first approximation of the torsion scalar potential the field equations are reduced to a Klein-Gordon type field equation for the torsion potential and the electromagnetic wave equation.A planar symmetric solution representing a parallel plates electric capacitor interacting with the electric field is given.The photon mass is proportional to the torsion potential and in the time dependent case the angular momentum is computed and is shown to be connected with torsion in analogy with the spin-torsion relation which appears in Einstein-Cartan gravity.When the curvature Ricci scalar is introduced we are able to show that the torsion potential can be associated with Higgs massive vectorial bosons.