Related papers: Vortex counting and the quantum Hall effect
A new approach to the quantization of Chern-Simons theory has been developed in recent papers of the author. It uses a "simulation" of the moduli space of flat connections modulo the gauge group which reveals to be related to a lattice…
Noncommutative Chern-Simons gauge theory coupled to nonrelativistic scalars or spinors is shown to admit the ``exotic'' two-parameter-centrally extended Galilean symmetry, realized in a unique way consistent with the Seiberg-Witten map.…
We present a series of existence theorems for multiple vortex solutions in the Gudnason model of the ${\cal N}=2$ supersymmetric field theory where non-Abelian gauge fields are governed by the pure Chern--Simons dynamics at dual levels and…
Non-Abelian vortices in six spacetime dimensions are obtained for a supersymmetric U(N) gauge theory with N hypermultiplets in the fundamental representation. Massless (moduli) fields are identified and classified into Nambu-Goldstone and…
We investigate the spectrum of the gauge theory with Chern-Simons term on the noncommutative plane, a modification of the description of the Quantum Hall fluid recently proposed by Susskind. We find a series of the noncommutative massive…
We apply the adiabatic approximation to investigate the low energy dynamics of vortices in the parity invariant double self-dual Higgs model with only mutual Chern-Simons interaction. When distances between solitons are large they are…
We evaluate the ground state degeneracy of noncommutative Chern-Simons models on the two-torus, a quantity that is interpreted as the "topological order" of associated phases of Hall fluids. We define the noncommutative theory via T-duality…
We investigate the structure of the moduli space of multiple BPS non-Abelian vortices in U(N) gauge theory with N fundamental Higgs fields, focusing our attention on the action of the exact global (color-flavor diagonal) SU(N) symmetry on…
This paper further develops the combinatorial approach to quantization of the Hamiltonian Chern Simons theory advertised in \cite{AGS}. Using the theory of quantum Wilson lines, we show how the Verlinde algebra appears within the context of…
We determine the dimension of the moduli space of non-Abelian vortices in Yang-Mills-Chern-Simons-Higgs theory in 2+1 dimensions for gauge groups $G=({\rm U}(1)\times G')/\mathbb{Z}_{n_0}$ with $G'$ being an arbitrary semi-simple group and…
We extend equivariant dimensional reduction techniques to the case of quantum spaces which are the product of a Kaehler manifold M with the quantum two-sphere. We work out the reduction of bundles which are equivariant under the natural…
Vortices produce locally concentrated field configurations and are solutions to the nonlinear partial differential equations systems of complicated structures. In this paper, we establish the existence and uniqueness for solutions of the…
Gauged linear sigma-models at critical coupling on Riemann surfaces yield self-dual field theories, their classical vacua being described by the vortex equations. For local models with structure group ${\rm U}(r)$, we give a description of…
Using the formalism of discrete quantum group gauge theory, one can construct the quantum algebras of observables for the Hamiltonian Chern-Simons model. The resulting moduli algebras provide quantizations of the algebra of functions on the…
We discuss ensemble averages of two-dimensional conformal field theories associated with an arbitrary indefinite lattice with integral quadratic form $Q$. We provide evidence that the holographic dual after the ensemble average is the…
The model of nonrelativistic particles coupled to nonstandard (2+1)-gravity [1] is extended to include Abelian or non-Abelian charges coupled to Chern-Simons gauge fields. Equivalently, the model may be viewed as describing the (Abelian or…
We propose a global model which accounts for all the observed quantum Hall states in terms of an abelian doublet of Chern-Simons gauge fields, with the strength of the Chern-Simons term given by a coupling matrix. The model is employed…
Quantum Hall inter-plateaux transitions are physical exemplars of quantum phase transitions. Near each of these transitions, the measured electrical conductivity scales with the same correlation length and dynamical critical exponents,…
We study the various quantum aspects of the $N=2$ supersymmetric Maxwell Chern-Simons vortex systems. The fermion zero modes around the vortices will give rise the degenerate states of vortices. We analyze the angular momentum of these zero…
For the abelian self-dual Chern-Simons-Higgs model we address existence issues of periodic vortex configurations -- the so-called condensates-- of non-topological type as $k \to 0$, where $k>0$ is the Chern-Simons parameter. We provide a…