Related papers: Bogomol'nyi Bounds for Two-Dimensional Lattice Sys…
Following a brief review of known vortex solutions in SU(N) gauge-adjoint Higgs theories we show the existence of a new ``minimal'' vortex solution in SU(3) gauge theory with two adjoint Higgs bosons. At a critical coupling the vortex…
We note that the Bogomolny equation for abelian vortices is precisely the condition for invariance of the Hermitian-Einstein equation under a degenerate conformal transformation. This leads to a natural interpretation of vortices as…
In this paper, we consider two types of topological solitons in a generalized Born-Infeld-Higgs model. We explore the self-dual structure of the model and prove the existence of planar vortex solutions. Furthermore, we couple the system…
We present a generic and systematic approach for constructing D-dimensional lattice models with exactly solvable d-dimensional boundary states localized to corners, edges, hinges and surfaces. These solvable models represent a class of…
We present a study of the 3d O(2) non-linear $\sigma$-model on the lattice, which exhibits topological defects in the form of vortices. They tend to organize into vortex lines that bear close analogies with global cosmic strings. Therefore,…
We prove Lieb-Robinson bounds for the dynamics of systems with an infinite dimensional Hilbert space and generated by unbounded Hamiltonians. In particular, we consider quantum harmonic and certain anharmonic lattice systems.
We construct and analyze a class of one-dimensional boundary Hamiltonians arising from two-dimensional symmetry-protected topological phases with $\mathbb{Z}_N^{\times 3}$ symmetry on a triangular lattice. Using a cohomology-based…
The spatial distribution of fields and currents in confining theories can give direct evidence of dual superconductivity. We review the behavior of vortices in the lattice Higgs effective theory. We discuss the techniques for finding these…
At Bradlow's limit, the moduli space of Bogomol'nyi vortices on a compact Riemann surface of genus $g$ is determined. The K\"{a}hler form, and the volume of the moduli space is then computed. These results are compared with the…
In this work we study a nonlinear gauged O(3)-sigma model with both minimal and nonminimal coupling in the covariant derivative. Using an asymmetric scalar potential, the model is found to exhibit both topological and non-topological…
We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. We propose an update…
We consider a gauged $CP(2)$ theory in the presence of the Chern-Simons action, focusing our attention on those time-independent solutions possessing radial symmetry. In this context, we develop a coherent first-order framework via the…
We study BPS string-like solutions in the 3+1 dimensional gauged CP(1) non-linear sigma model. The same analysis can be applied to study instantons in 2 euclidean dimensions. We use the moduli matrix approach to construct analytically the…
A hyperbolic lattice allows for any $p$-fold rotational symmetry, in stark contrast to a two-dimensional crystalline material, where only twofold, threefold, fourfold or sixfold rotational symmetry is permitted. This unique feature…
It is known that optical-lattice (OL) potentials can stabilize solitons and solitary vortices against the critical collapse, generated by the cubic attractive nonlinearity in the 2D geometry. We demonstrate OLs can also stabilize various…
The existence and stability of solitons in Bose-Einstein condensates with attractive inter-atomic interactions, described by the Gross-Pitaevskii equation with a three-dimensional (3D) periodic potential, are investigated in a systematic…
We study moduli spaces of solutions to the extended Bogomolny equations on $\Sigma \times \mathbb{R_{+,y}}$ with gauge group $\operatorname{SL}(2,\mathbb{C})$ satisfying the generalized Nahm pole boundary condition as $y\to 0$ and limiting…
We study the configuration space of the Tomboulis $SO(3) \times Z(2)$ formulation with periodic boundary conditions. The dynamical variables are constrained by the required coincidence of Z(2) and SO(3) monopoles. Furthermore, there is an…
It is shown that the SU(2) semilocal model -- the Abelian Higgs model with two complex scalars -- admits a new class of stationary, straight string solutions carrying a persistent current and having finite energy per unit length. In the…
We investigate the existence of self-dual configurations in the restricted gauged baby Skyrme model enlarged with a $Z_2$--symmetry, which introduces a real scalar field. For such a purpose, we implement the Bogomol'nyi procedure that…