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We propose a twisted SUSY invariant formulation of Chern-Simons theory on a Euclidean three dimensional lattice. The SUSY algebra to be realized on the lattice is the N=4 D=3 twisted algebra that was recently proposed by D'Adda et al.. In…

We show that Chern-Simons gauge theory with appropriate cutoffs is equivalent, term by term in perturbation theory, to a Fermionic theory with a nonlocal interaction term. When an additional cutoff is placed on the Fermi fields, this…

In a somewhat overlooked work by Seiberg, a definition of the topological charge for SU(N) lattice fields was given. Here, it is shown that Seibergs and L\"{u}schers charge definition are related up to the section of the bundle. With the…

We couple three-dimensional Chern-Simons gauge theory with BF theory and study deformations of the theory by means of the antifield BRST formalism. We analyze all possible consistent interaction terms for the action under physical…

We study several different $Z_2$ topological ordered states in frustrated spin systems. The effective theories for those different Z_2 topological orders all have the same form -- a Z_2 gauge theory which can also be written as a mutual…

We present effective field theories for dipole symmetric topological matters that can be described by the Chern-Simons theory. Unlike most studies using higher-rank gauge theory, we develop a framework with both U(1) and dipole gauge…

We analyse the pure Chern-Simons theory on an Euclidean infinite lattice. We point out that, as a consequence of its symmetries, the Chern-Simons theory does not have an integrable kernel. Due to the linearity of the action in the…

We introduce a technique to construct gapped lattice models using defects in topological field theory. We illustrate with 2+1 dimensional models, for example Chern-Simons theories. These models are local, though the state space is not…

We construct the Hamiltonian description of the Chern-Simons theory with Z_n gauge group on a triangular lattice. We show that the Z_2 model can be mapped onto free Majorana fermions and compute the excitation spectrum. In the bulk the…

It is shown that U(1) chiral gauge theories with anomaly-free multiplets of Weyl fermions can be put on the lattice without breaking the gauge invariance or violating any other fundamental principle. The Ginsparg-Wilson relation plays a key…

The topological non-Abelian Chern-Simons theory with a boundary is shown to require a scalar field companion in order to preserve overall gauge-invariance both in the 3 dimensional manifold, as well as on its boundary. This scalar field,…

We study observables and deformations of generalized Chern-Simons action and show how to apply these results to maximally supersymmetric gauge theories. We describe a construction of large class of deformations based on some results on the…

The Green functions of the Chern-Simons theory quantized in the axial gauge are shown to be calculable as the unique, exact solution of the Ward identities which express the invariance of the theory under the topological supersymmetry of…

Taking as starting point a perturbative study of the classical equations of motion of the non-Abelian Chern-Simons Theory with non-dynamical sources, we search for analytical expressions for link invarians. In order to present these…

We show that the classical non-abelian pure Chern-Simons action is related in a natural way to completely integrable systems of the Davey-Stewartson hyerarchy, via reductions of the gauge connection in Hermitian spaces and by performing…

We formulate lattice perturbation theory for gauge theories in noncommutative geometry. We apply it to three-dimensional noncommutative QED and calculate the effective action induced by Dirac fermions. In particular "parity invariance" of a…

Chern-Simons theory coupled to complex scalars is quantized on the light- front in the local light-cone gauge by constructing the self-consistent hamiltonian theory. It is shown that no inconsistency arises on using two local gauge-fixing…

We study the structure and properties of vortices in a recently proposed Abelian Maxwell-Chern-Simons model in $2 +1 $ dimensions. The model which is described by gauge field interacting with a complex scalar field, includes two parity and…

A recently proposed formulation of chiral lattice gauge theories is reviewed, in which the locality and gauge invariance of the theory can be preserved if the fermion representation of the gauge group is anomaly-free.

Starting from a $D=3$, $N=4$ supersymmetric theory for matter fields, a twist with a Grassmann parity change is defined which maps the theory into a gauge fixed, abelian $BF$ theory on curved 3-manifolds. After adding surface terms to this…