Distinguishing k-defects from their Canonical Twins

We study k-defects—topological defects in theories with more than two derivatives and second-order equations of motion—and describe some striking ways in which these defects both resemble and differ from their analogues in canonical scalar field theories. We show that, for some models, the homotopy structure of the vacuum manifold is insufficient to establish the existence of k-defects, in contrast to the canonical case. These results also constrain certain families of Dirac-Born-Infeld instanton solutions in the 4-dimensional effective theory. We then describe a class of k-defect solutions, which we dub ‘‘doppelgängers,’’ that precisely match the field profile and energy density of their canonical scalar field theory counterparts. We give a complete characterization of Lagrangians which admit doppelgänger domain walls. By numerically computing the fluctuation eigenmodes about domain wall solutions, we find different spectra for doppelgängers and canonical walls, allowing us to distinguish between k-defects and the canonical walls they mimic. We search for doppelgängers for cosmic strings by numerically constructing solutions of Dirac-Born-Infeld and canonical scalar field theories. Despite investigating several examples, we are unable to find doppelgänger cosmic strings, hence the existence of doppelgängers for defects with codimension >1 remains an open question.