Examples of Embedded Defects (in Particle Physics and Condensed Matter)

We present a series of examples designed to clarify the formalism of the companion paper `Embedded Vortices'. After summarising this formalism in a prescriptive sense, we run through several examples: firstly, deriving the embedded defect spectrum for Weinberg-Salam theory, then discussing several examples designed to illustrate facets of the formalism. We then calculate the embedded defect spectrum for three physical Grand Unified Theories and conclude with a discussion of vortices formed in the superfluid $^3$He-A phase transition.