Related papers: Hopf instantons in Chern-Simons theory

We use ideas on integrability in higher dimensions to define Lorentz invariant field theories with an infinite number of local conserved currents. The models considered have a two dimensional target space. Requiring the existence of…

By performing the canonical quantization of the Abelian Chern-Simons model on the light-front (as suggested by Dirac), we clarify some controversies appearing in recent papers that discuss the relation between the existence of excitations…

We construct an infinite number of exact time dependent soliton solutions, carrying non-trivial Hopf topological charges, in a 3+1 dimensional Lorentz invariant theory with target space S^2. The construction is based on an ansatz which…

We derive a rigorous, quantum mechanical map of fermionic creation and annihilation operators to continuous Cartesian variables that exactly reproduces the matrix structure of the many-fermion problem. We show how our scheme can be used to…

Reducing a 3-dimensional Chern-Simons term by a symmetry yields other topologically interesting structures. Specifically, reducing by radial symmetry results in a 1-dimensional quantum mechanical model, which has recently been used in an…

Various applications of Chern-Simons theory in algebraic topology, in particular knot theory, condensed matter physics and cosmology are reviewed. Special attention is paid to appearances of Chern-Simons actions in the theory of the…

Magnetic hopfions are three-dimensional topological solitons with non-zero Hopf index ${\cal H}$ in the vector field of material's local magnetization. In this Letter elliptical stability of hopfions with ${\cal H}=1$ in a classical…

We study Chern-Simons (CS) superconductivity in the presence of uniform external magnetic field of {\it arbitrary strength} for a system of fermions in two spatial dimensions, which are minimally coupled both to the CS and Maxwell gauge…

We study the anomalous dimensions for scalar operators for a three-dimensional Chern-Simons theory recently proposed in arXiv:0806.1218. We show that the mixing matrix at two-loop order is that for an integrable Hamiltonian of an SU(4) spin…

We revisit the implementation of the metric-independent Fock-Schwinger gauge in the abelian Chern-Simons field theory defined in ${\mathbb{R}}^3$ by means of a homotopy condition. This leads to the lagrangian $F \wedge hF$ in terms of…

We exhaustively construct instanton solutions and elucidate their properties in one-dimensional anti-ferromagnetic chiral magnets based on the $O(3)$ nonlinear sigma model description of spin chains with the Dzyaloshinskii-Moriya (DM)…

We prove the existence of topological solutions to the self-dual Chern-Simons model and the Abelian Higgs system on the lattice graphs Z^n for n>1. This extends the results in Huang, Lin and Yau [HLY20] from finite graphs to lattice graphs.

This is a brief summary of our studies of quantum field theories in a special limit in which the instantons are present, the anti-instantons are absent, and the perturbative corrections are reduced to one-loop. We analyze the corresponding…

We consider the bosonic sector of a N=2 supersymmetric Chern-Simons-Higgs theory in 2+1 dimensions. The gauge group is U(1)xU(N) and has N_f flavors of fundamental matter fields. The model supports non-Abelian (axially symmetric) vortices…

The Chern-Simons theories on a noncommutative plane, which is shown to be describing the quantum Hall liquid, is considered. We introduce matter fields fundamentally coupled to the noncommutative Chern-Simons field. Exploiting BPS equations…

We study the higher Frobenius-Schur indicators of modules over semisimple Hopf algebras, and relate them to other invariants as the exponent, the order, and the index. We prove various divisibility and integrality results for these…

We study large $N$ 2+1 dimensional fermions in the fundamental representation of an $SU(N)_k$ Chern Simons gauge group in the presence of a uniform background magnetic field for the $U(1)$ global symmetry of this theory. The magnetic field…

We introduce new three-dimensional topological phases of two-band models using the Pontryagin-Thom construction. In symmetry class A these are the infinitely many Hopf-Chern topological insulators, which are hybrids of layered Chern…

This is primarily a survey of the way in which Hopf cyclic cohomology has emerged and evolved, in close relationship with the application of the noncommutative local index formula to transverse index theory on foliations. Being…

We consider electrons in two dimensions in a strong magnetic field at half filling of the lowest Landau level using the Chern-Simons approach. Starting from a lattice Hamiltonian for the electrons, we derive a path integral (PI) formulation…