Embedded Defects

We give a prescription for embedding classical solutions and, in particular, topological defects in field theories which are invariant under symmetry groups that are not necessarily simple. After providing examples of embedded defects in field theories based on simple groups, we consider the electroweak model and show that it contains the $Z$ string and a one parameter family of strings called the $W(\alpha )$ string. It is argued that, although the members of this family are gauge equivalent when considered in isolation, each member should be considered distinct when multi-string solutions are considered. We then turn to the issue of stability of embedded defects and demonstrate the instability of a large class of such solutions in the absence of bound states or condensates. The $Z$ string is shown to be unstable when the Weinberg angle ($\theta_w$) is $\pi /4$ for all values of the Higgs mass. The $W$ strings are also shown to be unstable for a large range of parameters. Embedded monopoles suffer from the Brandt-Neri-Coleman instability. A simple physical understanding of this instability is provided in terms of the phenomenon of W-condensation. Finally, we connect the electroweak string solutions to the sphaleron: ``twisted'' loops of W string and finite segments of W and Z strings collapse into the sphaleron configuration, at least, for small values of $\theta_w$.Comment: tex, 28 page

Doppelganger defects

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.Comment: 27 pages, 4 figure

Native defects in ultra-high vacuum grown graphene islands on Cu(111)

We present a scanning tunneling microscopy (STM) study of native defects in graphene islands grown by ultra-high vacuum (UHV) decomposition of ethylene on Cu(111). We characterize these defects through a survey of their apparent heights, atomic-resolution imaging, and detailed tunneling spectroscopy. Bright defects that occur only in graphene regions are identified as C site point defects in the graphene lattice and are most likely single C vacancies. Dark defect types are observed in both graphene and Cu regions, and are likely point defects in the Cu surface. We also present data showing the importance of bias and tip termination to the appearance of the defects in STM images and the ability to achieve atomic resolution. Finally, we present tunneling spectroscopy measurements probing the influence of point defects on the local electronic landscape of graphene islands.Comment: 16 pages, 5 figure

Algebraic approach to multiple defects on the line and application to Casimir force

An algebraic framework for quantization in presence of arbitrary number of point-like defects on the line is developed. We consider a scalar field which interacts with the defects and freely propagates away of them. As an application we compute the Casimir force both at zero and finite temperature. We derive also the charge density in the Gibbs state of a complex scalar field with defects. The example of two delta-defects is treated in detail.Comment: 24 pages, 10 figure