Band structure in classical field theory

Stability and instability bands in classical mechanics are well-studied in connection with systems such as described by the Mathieu equation. We examine whether such band structure can arise in classical field theory in the context of an embedded kink in 1+1 dimensions. The static embedded kink is unstable to perturbations but we show that if the kink is dynamic it can exhibit stability in certain parameter bands. Our results are relevant for estimating the lifetimes of various embedded defects and, in particular, loops of electroweak Z-string.Comment: 6 pages, 4 fig. Reference added, Fig. 3 updated with improved numerical code, minor comments added. Version to be published in Phys. Rev.

Electroweak Strings, Zero Modes and Baryon Number

The Dirac equations for leptons and quarks in the background of an electroweak $Z-$string have zero mode solutions. If two loops of electroweak string are linked, the zero modes on one of the loops interacts with the other loop via an Aharanov-Bohm interaction. The effects of this interaction are briefly discussed and it is shown that the fermions induce a baryon number on linked loops of $Z-$string. (Submitted to Proceedings of "Trends in Astrophysics" Conference, Stockholm, 1994.)Comment: LaTeX using espcrc2.sty (version 2.5) (hit return on error messages), 3 page

Open/Closed String Topology and Moduli Space Actions via Open/Closed Hochschild Actions

In this paper we extend our correlation functions to the open/closed case. This gives rise to actions of an open/closed version of the Sullivan PROP as well as an action of the relevant moduli space. There are several unexpected structures and conditions that arise in this extension which are forced upon us by considering the open sector. For string topology type operations, one cannot just consider graphs, but has to take punctures into account and one has to restrict the underlying Frobenius algebras. In the moduli space, one first has to pass to a smaller moduli space which is closed under open/closed duality and then consider covers in order to account for the punctures

Electroweak String Configurations with Baryon Number

In the context of electroweak strings, the baryon number anomaly equation may be reinterpreted as a conservation law for baryon number minus helicity. Since the helicity is a sum of the link and twist numbers, linked or twisted loops of electroweak string carry baryon number. We evaluate the change in the baryon number obtained by delinking loops of electroweak $Z-$string and show that twisted electroweak string segments may be regarded as extended sphalerons. We also suggest an alternative scenario for electroweak baryogenesis.Comment: 11 pages, figure available on request. Added discussion of string-sphaleron connection for non-vanishing Weinberg angle and shortened discussion on formation of linked configuration

Spectra of Magnetic Fields Injected during Baryogenesis

Helical magnetic fields are injected into the cosmic medium during cosmological baryogenesis and can potentially provide a useful probe of the early universe. We construct a model to study the injection process during a first order phase transition and to determine the power spectra of the injected magnetic field. By Monte Carlo simulations we evaluate the Fourier space symmetric and helical power spectra of the magnetic field at the time the phase transition completes. The spectra are peaked at the scale given by the inverse size of bubbles at percolation and with a comparable width. These injected magnetic fields set the initial conditions for further cosmological magneto-hydrodynamical evolution.Comment: 8 pages, 9 figures; revised discussion and added new references; version accepted for publication in PR

Helical Magnetic Fields from Sphaleron Decay and Baryogenesis

Many models of baryogenesis rely on anomalous particle physics processes to give baryon number violation. By numerically evolving the electroweak equations on a lattice, we show that baryogenesis in these models creates helical cosmic magnetic fields. After a transitory period, electroweak dynamics is found to conserve the Chern-Simons number and the total electromagnetic helicity. We argue that baryogenesis could lead to magnetic fields of nano-Gauss strength today on astrophysical length scales. In addition to being astrophysically relevant, such helical magnetic fields can provide an independent probe of baryogenesis and CP violation in particle physics.Comment: 4 pages, 1 figure. Added references, fixed typo

Electroweak Dyons

We consider dyon configurations in the standard electroweak model. In the presence of a $\theta$ term and no fermions, the usual result $q = (n+\theta /2\pi ) e$ is obtained for the electric charge spectrum. The effect of including standard model fermions is discussed qualitatively.Comment: 14 pages, TUTP-94-1

Topological Incarnations of Electroweak Defects

We propose a criterion to classify hybrid defects occurring in field theoretic models such as the standard electroweak model. This criterion leads us to consider the minimal extension of the electroweak model in which electroweak magnetic monopoles and $Z$-strings are topological. We briefly discuss the cosmology of such defects.Comment: 12 pages + 1 figure; LaTe

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.Comment: final corrections. latex fil