Dynamical Lorentz symmetry breaking and topological defects

TL;DR

This paper explores the existence of topological defect solutions in field theories with tensor fields that spontaneously break Lorentz symmetry, identifying specific tensor types capable of supporting such defects and discussing their potential detectability.

Contribution

It identifies which tensor fields can support topological defects in Lorentz-violating theories and constructs explicit solutions for vectors and antisymmetric two-tensors.

Findings

Vector domain wall solutions constructed

Antisymmetric tensor monopole solutions identified

Monopoles potentially detectable via gravitational lensing

Abstract

I discuss the possibility of topological defect solutions in field theories containing a tensor field which spontaneously breaks Lorentz symmetry. I find that for theories of a tensor with rank r <= 5 and for which the vacuum manifold consists of the tensors whose "square" is some constant value, only three types of tensor (vectors, antisymmetric two-tensors, and symmetric two-tensors) have the appropriate vacuum manifold topology to support topological defects. Of these, topological defect solutions can be easily constructed for two: vector domain wall solutions and antisymmetric tensor monopole solutions. These antisymmetric tensor monopole solutions are in principle detectible via their gravitational lensing effects.