Related papers: A remark on low regularity solutions of the Chern-…
We find the inconsistency of dimensional reduction and naive dimensional regularization in their applications to Chern-Simons type gauge theories. Further we adopt a consistent dimensional regularization to investigate the quantum…
In this paper we prove a rigidity result for a solution to the non self-dual Chern--Simons--Schr{\"o}dinger equation at the level of the soliton.
We consider the initial-value problem for the Chern-Simons-Schr\"odinger system, which is a gauge-covariant Schr\"{o}dinger system in $\mathbb{R}_t\times\mathbb{R}^2_x$ with a long-range electromagnetic field. We show that, in the Coulomb…
The equivalence between the Chern-Simons gauge theory on a three-dimensional manifold with boundary and the WZNW model on the boundary is established in a simple and general way using the BRST symmetry. Our approach is based on restoring…
The Klein-Gordon-Schr\"odinger system in 3D is shown to be locally well-posed for Schr\"odinger data in H^s and wave data in H^{\sigma} \times H^{\sigma -1}, if s > - 1/4, \sigma > - 1/2, \sigma -2s > 3/2 and \sigma -2 < s < \sigma +1 .…
We conjecture a new sequence of dualities between Chern-Simons gauge theories simultaneously coupled to fundamental bosons and fermions. These dualities reduce to those proposed by Aharony when the number of bosons or fermions is zero. Our…
In these notes, we present an alternative version of discrete Dirac mechanics using Dirac structures. We first establish a notion of 'continuous Dirac system' and then propose a definition of discrete Dirac system, proving that it is…
The self-dual systems are constrained and so are simpler to understand. In recent years there have been several studies on the self-dual Chern-Simons systems. Here I present a brief survey of works done by my collaborators and myself. I…
Considering three-dimensional Chern-Simons theory, either coupled to matter or with a Yang-Mills term, we show the validity of a trace identity, playing the role of a local form of the Callan-Symanzik equation, in all orders of perturbation…
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…
A novel approach to the analysis of a noncommutative Chern--Simons gauge theory with matter coupled in the adjoint representation has been discussed. The analysis is based on a recently proposed closed form Seiberg--Witten map which is…
We propose a gauge-invariant system of the Chern-Simons-Schrodinger type on a one-dimensional lattice. By using the spatial gauge condition, we prove local and global well-posedness of the initial-value problem in the space of square…
A method for removing fermion doublers in anomaly free chiral gauge theories on the lattice is proposed. It is proven that the resulting continuum theory is gauge invariant and does not require noninvariant counterterms of fine tuning of…
The Dirac quantization procedure of a magnetic monopole can be used to derive the coefficient of the D=3 Chern-Simons term through a self-consistency argument, which can be readily generalized to any odd D. This yields consistent and…
This paper aims to establish counterparts of fundamental regularity statements for solutions to elliptic equations in the setting of low-dimensional structures such as, for instance, glued manifolds or CW-complexes. The main result proves…
We show the smoothness of weakly Dirac-harmonic maps from a closed spin Riemann surface into stationary Lorentzian manifolds, and obtain a regularity theorem for a class of critical elliptic systems without anti-symmetry structures.
We study a system of equations arising in the Chern-Simons model on finite graphs. Using the iteration scheme and the upper and lower solutions method, we get existence of solutions in the non-critical case. The critical case is dealt with…
In this paper, we show the global existence and uniqueness of classical solutions of the Maxwell-Chern-Simmons-Higgs system coupled to a neutral scalar with nontrivial scalar potential on (2+1) dimensional Minkowski spacetime. Our methods…
The normal phase of the high-$T_c$ cuprates is apparently not described by Fermi liquid theory. It has been proposed that a dynamically generated gauge field must appear in the effective field theory. Even a simple spinon-gauge system is…
In this paper, we consider the initial-boundary value problem for the time-dependent Maxwell--Schr\"{o}dinger equations in the Coulomb gauge. We first prove the global existence of weak solutions to the equations. Next we propose an…