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Register a new userMagnetic structures and Z_2 vortices in a non-Abelian gauge model
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The magnetic order of the triangular lattice with antiferromagnetic interactions is described by an SO(3) field and allows for the presence of Z2 magnetic vortices as defects. In this work we show how these Z2 vortices can be fitted into a local SU(2) gauge theory. We propose simple Ansu007fatzes for vortex configurations and calculate their energies using well-known results of the Abelian gauge model. We comment on how Dzyaloshinskii-Moriya interactions could be derived from a non-Abelian gauge theory and speculate on their effect on non trivial configurations.
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A brane-world $SU(5)$ GUT model with global non-Abelian vortices is constructed in six-dimensional spacetime. We find a solution with a vortex associated to $SU(3)$ separated from another vortex associated to $SU(2)$. This $3-2$ split configuration achieves a geometric Higgs mechanism for $SU(5)to SU(3)times SU(2)times U(1)$ symmetry breaking. A simple deformation potential induces a domain wall between non-Abelian vortices, leading to a linear confining potential. The confinement stabilizes the vortex separation moduli, and assures the vorticity of $SU(3)$ group and of $SU(2)$ group to be identical. This dictates the equality of the numbers of fermion zero modes in the fundamental representation of $SU(3)$ (quarks) and of $SU(2)$ (leptons), leading to quark-lepton generations. The standard model massless gauge fields are localized on the non-Abelian vortices thanks to a field-dependent gauge kinetic function. We perform fluctuation analysis with an appropriate gauge fixing and obtain a four-dimensional effective Lagrangian of unbroken and broken gauge fields at quadratic order. We find that $SU(3) times SU(2) times U(1)$ gauge fields are localized on the vortices and exactly massless. Complications in analyzing the spectra of gauge fields with the nontrivial gauge kinetic function are neatly worked out by a vector-analysis like method.
The vortex solutions of various classical planar field theories with (Abelian) Chern-Simons term are reviewed. Relativistic vortices, put forward by Paul and Khare, arise when the Abelian Higgs model is augmented with the Chern-Simons term. Adding a suitable sixth-order potential and turning off the Maxwell term provides us with pure Chern-Simons theory with both topological and non-topological self-dual vortices, as found by Hong-Kim-Pac, and by Jackiw-Lee-Weinberg. The non-relativistic limit of the latter leads to non-topological Jackiw-Pi vortices with a pure fourth-order potential. Explicit solutions are found by solving the Liouville equation. The scalar matter field can be replaced by spinors, leading to fermionic vortices. Alternatively, topological vortices in external field are constructed in the phenomenological model proposed by Zhang-Hansson-Kivelson. Non-relativistic Maxwell-Chern-Simons vortices are also studied. The Schroedinger symmetry of Jackiw-Pi vortices, as well as the construction of some time-dependent vortices, can be explained by the conformal properties of non-relativistic space-time, derived in a Kaluza-Klein-type framework.
Non-Abelian flux-tube (string) solutions carrying global currents are found in the bosonic sector of 4-dimensional N=2 super-symmetric gauge theories. The specific model considered here posseses U(2)local x SU(2)global symmetry, with two scalar doublets in the fundamental representation of SU(2). We construct string solutions that are stationary and translationally symmetric along the x3 direction, and they are characterized by a matrix phase between the two doublets, referred to as twist. Consequently, twisted strings have nonzero (global) charge, momentum, and in some cases even angular momentum per unit length. The planar cross section of a twisted string corresponds to a rotationally symmetric, charged non-Abelian vortex, satisfying 1st order Bogomolny-type equations and 2nd order Gauss-constraints. Interestingly, depending on the nature of the matrix phase, some of these solutions even break rotational symmetry in R3. Although twisted vortices have higher energy than the untwisted ones, they are expected to be linearly stable since one can maintain their charge (or twist) fixed with respect to small perturbations.
We study the properties of a single magnetic vortex and magnetic vortex lattices in a generalization of the Abelian Higgs model containing the simplest derivative interaction that preserves the $U(1)$ gauge symmetry of the original model. The paper is motivated by the study of finite isospin chiral perturbation theory in a uniform, external : since pions are Goldstone bosons of QCD (due to chiral symmetry breaking by the QCD vacuum), they interact through momentum dependent terms. We introduce a uniform external magnetic field and find the asymptotic properties of single vortex solutions and compare them to the well-known solutions of the standard Abelian Higgs Model. Furthermore, we study the vortex lattice solutions near the upper critical field using the method of successive approximations, which was originally used by Abrikosov in his seminal paper on type-II superconductors. We find the vortex lattice structure, which remains hexagonal as in the standard Abelian Higgs model, and condensation energy of the vortex lattices relative to the normal vacuum (in a uniform magnetic field).
Basis tensor gauge theory is a vierbein analog reformulation of ordinary gauge theories in which the difference of local field degrees of freedom has the interpretation of an object similar to a Wilson line. Here we present a non-Abelian basis tensor gauge theory formalism. Unlike in the Abelian case, the map between the ordinary gauge field and the basis tensor gauge field is nonlinear. To test the formalism, we compute the beta function and the two-point function at the one-loop level in non-Abelian basis tensor gauge theory and show that it reproduces the well-known results from the usual formulation of non-Abelian gauge theory.
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