Related papers: Matrix model and noncommutative Chern-Simons theor…
We study topological phases of interacting systems in two spatial dimensions in the absence of topological order (i.e. with a unique ground state on closed manifolds and no fractional excitations). These are the closest interacting analogs…
We discuss non commutative functions, which naturally arise when dealing with functions of more than one matrix variable.
In this paper a class of multi-Chern-Simons field theories which is relevant to the statistical mechanics of polymer systems is investigated. Motivated by the problems which one encounters in the treatment of these theories, a general…
We study the interconnection between the finite projective modules for a fuzzy sphere, determined in a previous paper, and the matrix model approach, making clear the physical meaning of noncommutative topological configurations.
A review of the relationships between matrix models and noncommutative gauge theory is presented. A lattice version of noncommutative Yang-Mills theory is constructed and used to examine some generic properties of noncommutative quantum…
In this article we further the study of non-commutative motives. Our main result is the construction of a simple model, given in terms of infinite matrices, for the suspension in the triangulated category of non-commutative motives. As a…
Noncommutative Chern - Simons' system is non-perturbatively investigated at a full deformed level. A deformed "commutative" phase space is found by a non-canonical change between two sets of deformed variables of noncommutative space. It is…
Robust zero modes supported by defects is one of the key features of topological matter. Its presence renders a system topologically inhomegeneuous, thus having no well-defined global topological invariant. The quantities labeling different…
The quantized magnetic flux $\Phi=-4\pi N\sk, N=0,\pm1,...$ of non-topological vortices in the non-relativistic Chern-Simons theory is related to the topological degree of the $S^2\to S^2$ mapping defined by lifting the problem to the…
In this paper we continue the study of the model proposed in the previous paper hep-th/0002077. The model consist of a system of extended objects of diverse dimensionalities, with or without boundaries, with actions of the Chern-Simons form…
We introduce a Hamiltonian for fermions on a lattice and prove a theorem regarding its topological properties. We identify the topological criterion as a $\mathbb{Z}_2-$ topological invariant $p(\textbf{k})$ (the Pfaffian polynomial). The…
We consider the Dunne-Jackiw-Pi-Trugenberger model of a U(N) Chern-Simons gauge theory coupled to a nonrelativistic complex adjoint matter on noncommutative space. Soliton configurations of this model are related the solutions of the chiral…
We study ${\mathcal{N}}=2$ supersymmetric $U(N)$ Chern-Simons with $N_{f}$ fundamental and $N_{f}$ antifundamental chiral multiplets of mass $m$ in the complete parameter space spanned by $(g,\,m,\,N,\,N_{f})$, where $g$ denotes the…
We give a self-contained and enriched review about topology properties in the rapidly growing field of topological states of matter (TSM). This review is mainly focus on the beautiful interplay of topology mathematics and condensed matter…
We have conclusively established the duality between noncommutative Maxwell-Chern-Simons theory and Self-Dual model, the latter in ordinary spacetime, to the first non-trivial order in the noncommutativity parameter $\theta^{\mu\nu}$, with…
We outline two approaches to the construction of integrable hierarchies associated with the theory of Gromov - Witten invariants of smooth projective varieties. We argue that a comparison of these two approaches yields nontrivial…
The SW map problem is formulated and solved in the BRST cohomological approach. The well known ambiguities of the SW map are shown to be associated to distinct cohomological classes. This analysis is applied to the noncommutative…
We present simple examples of finite-dimensional connected homogeneous spaces (they are actually topological manifolds) with nonhomogeneous and nonrigid factors. In particular, we give an elementary solution of an old problem in general…
An all orders formula for the $S$-matrix for 2 $\rightarrow$ 2 scattering in large N Chern-Simons theory coupled to a fundamental scalar has recently been conjectured. We find a scaling limit of the theory in which the pole in this…
Using a coherent state representation we derive many-body probability distributions and wavefunctions for the Chern-Simons matrix model proposed by Polychronakos and compare them to the Laughlin ones. We analyze two different coherent state…