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The soliton structure of a gauge theory proposed to describe chiral excitations in the multi-Layer Fractional Quantum Hall Effect is investigated. A new type of derivative multi-component nonlinear Schr\"{o}dinger equation emerges as…
Recently proposed new gauge invariant formulation of the Chern-Simons gauge theory is considered in detail. This formulation is consistent with the gauge fixed formulation. Furthermore it is found that the canonical (Noether) Poincar\'e…
An extension of the AGT relation from two to three dimensions begins from connecting the theory on domain wall between some two S-dual SYM models with the 3d Chern-Simons theory. The simplest kind of such a relation would presumably connect…
We consider the construction of refined Chern-Simons torus knot invariants by M. Aganagic and S. Shakirov from the DAHA viewpoint of I. Cherednik. We give a proof of Cherednik's conjecture on the stabilization of superpolynomials, and then…
A new gauge invariant formulation of the relativistic scalar field interacting with Chern-Simons gauge fields is considered. This formulation is consistent with the gauge fixed formulation. Furthermore we find that canonical (Noether)…
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…
We construct a Chern-Simons action for q-deformed gauge theory which is a simple and straightforward generalization of the usual one. Space-time continues to be an ordinary (commuting) manifold, while the gauge potentials and the field…
We consider dimensional reduction of gauge theories with arbitrary gauge group in a formalism based on equivariant principal bundles. For the classical gauge groups we clarify the relations between equivariant principal bundles and quiver…
Two main gauge invariant off-shell models are studied in this Thesis. I) Poincare-invariant topological gravity in even dimensions is formulated as a transgression field theory whose gauge connections are associated to linear and nonlinear…
Chern-Weil and Chern-Simons theory extend to certain infinite-rank bundles that appear in mathematical physics. We discuss what is known of the invariant theory of the corresponding infinite-dimensional Lie groups. We use these techniques…
Large N duality conjecture between U(N) Chern-Simons gauge theory on $S^3$ and A-model topological string theory on the resolved conifold was verified at the level of partition function and Wilson loop observables. As a consequence, the…
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 the first of these two lectures, I describe a gauge theory approach to understanding quantum knot invariants as Laurent polynomials in a complex variable q. The two main steps are to reinterpret three-dimensional Chern-Simons gauge…
General relativity is extended by promoting the three-dimensional gravitational Chern-Simons term to four dimensions. This entails choosing an embedding coordinate v_\mu -- an external quantity, which we fix to be a non-vanishing constant…
We discuss several aspects of three dimensional N=2 supersymmetric gauge theories coupled to chiral multiplets. The generation of Chern-Simons couplings at low-energies results in novel behaviour including compact Coulomb branches,…
In 1999, Khovanov showed that a link invariant known as the Jones polynomial is the Euler characteristic of a homology theory. The knot categorification problem is to find a general construction of knot homology groups, and to explain their…
In the late 1980s Witten used the Chern-Simons form of a connection to construct new invariants of 3-manifolds and knots, recovering in particular the Jones invariants. Since then the associated topological quantum field theory (TQFT) has…
We study the most general renormalizable ${\cal N}=1$ $U(N)$ Chern-Simons gauge theory coupled to a single (generically massive) fundamental matter multiplet. At leading order in the 't Hooft large $N$ limit we present computations and…
We propose methods to construct gauge invariant decompositions of the nucleon spin, particularly gauge invariant descriptions of the gluon polarization. We show that gauge invariant decompositions of the nucleon spin can be derived…
A direct relation between two types of topological field theories, Chern-Simons theory and BF theory, is presented by using ``Generalized Differential Calculus'', which extends an ordinary p-form to an ordered pair of p and (p+1)-form. We…