Doppelganger defects

TL;DR

This paper explores topological k-defects in higher-derivative theories, revealing conditions for their existence, introducing doppelganger solutions that mimic canonical defects, and analyzing their stability and differences, especially for domain walls and cosmic strings.

Contribution

It characterizes conditions for k-defects, introduces doppelganger solutions that replicate canonical defect profiles, and distinguishes their spectra through numerical analysis.

Findings

Doppelganger domain walls match canonical profiles and energies.

Spectral differences allow distinguishing k-defects from canonical walls.

Doppelganger cosmic strings were not found despite extensive search.

Abstract

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 DBI instanton solutions in the 4-dimensional effective theory. We then describe a class of k-defect solutions, which we dub doppelgangers, 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 doppelganger domain walls. By numerically computing the fluctuation eigenmodes about domain wall solutions, we find different spectra for doppelgangers and canonical walls, allowing us to distinguish between k-defects and the canonical walls they mimic. We search for doppelgangers for cosmic strings by numerically constructing solutions of DBI and canonical scalar field theories. Despite investigating several examples, we are unable to find doppelganger cosmic strings, hence the existence of doppelgangers for defects with codimension >1 remains an open question.