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 $r\le 5$ 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.

• Received 13 August 2010

DOI:https://doi.org/10.1103/PhysRevD.82.125015