Chern-Simons Coefficient Research Articles

The Chern-Simons coefficient in supersymmetric Yang-Mills Chern-Simons theories

We study one-loop corrections to the Chern-Simons coefficient κ = k 4π in N = 1, 2, 3 supersymmetric Yang-Mills Chern-Simons systems. In the pure bosonic case, the shift of the parameter k is known to be k → k + c v , where c v is the quadratic Casimir of the gauge group. In the N = 1 case, the fermionic contribution cancels the bosonic contribution by half and the shift is k → k + c v 2 , making the theory anomalous if c v is odd. In the N = 2, 3 cases, the fermionic contribution cancels the bosonic contribution completely and there is no correction. We also calculate the mass corrections, and show that the supersymmetry is preserved. As the matter fields decouple from the gauge field in the pure Chern-Simons limit, this work sheds some light on the regularization dependency of the correction in pure Chern-Simons systems. We also discuss the implication to the case when the gauge symmetry is spontaneously broken by the Higgs mechanism.

FIRST AND SECOND ORDER PHASE TRANSITIONS IN MAXWELL–CHERN–SIMONS THEORY COUPLED TO FERMIONS

In the Maxwell–Chern–Simons theory coupled to Nf flavors of four-component fermions (or an even number of two-component fermions), we construct the gauge-covariant effective potential written in terms of two order parameters which are able to probe the breakdown of chiral symmetry and parity. In the absence of the bare Chern–Simons term, we show that the chiral symmetry is spontaneously broken for fermion flavors Nf below a certain finite critical number [Formula: see text] while the parity is not broken spontaneously. This chiral phase transition is of the second order. In the presence of the bare Chern–Simons term, on the other hand, the chiral phase transition associated with the spontaneous breaking of chiral symmetry is shown to continue to exist, although the parity is explicitly broken. However, it is shown that the existence of the bare Chern–Simons term changes the order of the chiral transition into the first order, no matter how small the bare Chern–Simons coefficient may be. This gauge-invariant result is consistent with that recently obtained through the Schwinger–Dyson equation in the nonlocal gauge.

Chern-Simons vortices in an open system.

A gauge invariant quantum field theory with a spacetime dependent Chern-Simons coefficient is studied. Using a constraint formalism together with the Schwinger action principle it is shown that non-zero gradients in the coefficient induce magnetic-moment corrections to the Hall current and transform vortex singularities into non-local objects. The fundamental commutator for the density fluctuations is obtained from the action principle and the Hamiltonian of the Chern-Simons field is shown to vanish only under the restricted class of variations which satisfy the gauge invariance constraint.

QED 2+1 with nonzero fermion density and the quantum Hall effect

A general expression for the conductivity in the QED 2+1 with nonzero fermion density in a uniform magnetic field is derived. It is shown that the conductivity is entirely determined by the Chern-Simons coefficient: σ ij = ε ij C and that it shows discrete steps as a function of the chemical potential and the magnetic field.

Integer quantization of the Chern-Simons coefficient in a broken phase

We consider a spontaneously broken nonabelian topologically massive gauge theory in a broken phase possessing a residual nonabelian symmetry. Recently there has been some question concerning the renormalization of the Chern-Simons coefficient in such a broken phase. We show that, in this broken vacuum, the renormalized ratio of the Chern-Simons coupling to the gauge coupling is shifted by 1 4π times an integer, preserving the usual integer quantization condition on the bare parameters.

The Chern-Simons coefficient in the Higgs phase

We study one-loop corrections to the Chern-Simons coefficient ϰ in abelian self-dual Chern-Simons Higgs systems and their N=2 and N=3 supersymmetric generalizations in both symmetric and asymmetric phases. One-loop corrections to the Chern-Simons coefficient of these systems turn out to be integer multiples of 1 4 π in both phases. Especially in the maximally supersymmetric N=3 case, the correction in the symmetric phase vanishes and that in the asymmetric phase is ϰ/(2 π| ϰ|). Our results suggest that nonabelian self-dual system might enjoy similar features. We also discuss various issues arising from our results.

Effect of rotation symmetry on Abelian Chern-Simons field theory and anyon equation on a sphere.

We analyze the Chern-Simons field theory coupled to non-relativistic matter field on a sphere using canonical transformation on the fields with special attention to the role of the rotation symmetry: SO(3) invariance restricts the Hilbert space to the one with a definite number of charges and dictates Dirac quantization condition to the Chern-Simons coefficient, whereas SO(2) invariance does not. The corresponding Schr\"odinger equation for many anyons (and for multispecies) on the sphere are presented with appropriate boundary condition. In the presence of an external magnetic monopole source, the ground state solutions of anyons are compared with monopole harmonics. The role of the translation and modular symmetry on a torus is also expounded.

Chern-Simons diffusion layers? Short wavelength dynamics determined by gauge invariance.

Uncoupled, classical Maxwell-Chern-Simons theory is studied in regions in which the Chern-Simons coefficient is a spacetime dependent quantity. Gauge invariance demands a modification of the strict Chern-Simons form in such a region. Behavior is governed by boundary and initial conditions. In many cases, the resulting [ital classical] behavior qualitatively resembles diffusive processes in statistical systems.

BOSONIC CHERN-SIMONS FIELD THEORY OF ANYON SUPERCONDUCTIVITY

We study the quantum field theory of non-relativistic bosons coupled to a Chern-Simons gauge field at nonzero particle density. This field theory is relevant to the study of anyon superconductors in which the anyons are described as bosons with a statistical interaction. We show that it is possible to find a mean field solution to the equations of motion for this system which has some of the features of Bose condensation. The mean field solution consists of a lattice of vortices each carrying a single quantum of statistical magnetic flux. We speculate on the effects of the quantum corrections to this mean field solution. We argue that the mean field solution is only stable under quantum corrections if the Chern-Simons coefficient N=2πθ/g2 is an integer. Consequences for anyon superconductivity are presented. A simple explanation for the Meissner effect in this system is discussed.

Radiatively induced Chern-Simons terms on the torus.

A Chern-Simons term is induced by integrating over fermions in the effective action of a (2+1)-dimensional field theory on a torus. It is shown that the Chern-Simons coefficient is functionally dependent on the nonintegrable phases of the torus as well as on the finite temperature and density. In the non-Abelian case such nonintegrable phases inhibit the generation of a Chern-Simons term in the most general case.

Chern-Simons Gauge Theory and Anyons at Finite Temperature

The temperature dependence of Chern-Simons coefficient and statistical angle are investigated by using field theory at finite temperature. The results show that the Chern-Simons term will melt away at high temperature and the statistical angle will increase as temperature increases. Temperature dependence of the filling fact for Landau-Level is also discussed.

BOGOMOL’NYI EQUATIONS FOR NON-ABELIAN CHERN-SIMONS-HIGGS THEORIES

We study the non-abelian Chern-Simons theory with spontaneous symmetry breaking. We find Bogomol’nyi type or self-dual equations for a particular choice of the Higgs potential; the corresponding vortex solutions for G=SU(2) carry both quantized electric charge Q= −en/2 and angular momentum J=nm2/4 (e is the fundamental charge, n is an integer associated with the Chern-Simons coefficient, and m is another integer which labels the topological sector). We propose a straightforward generalization to the SU(N) case.

Photon as a goldstone boson in (2 + 1)-dimensional abelian gauge theories

We examine the relationship between the masslessness of a photon and the realization of global symmetries in abelian gauge theories in 2 + 1 dimensions: scalar and spinor QED and their immediate generalizations. We find that this masslessness (in the Coulomb phase) directly follows from the spontaneous breakdown of a symmetry generated by the magnetic flux. In spinor QED with two flavours the chiral symmetry is broken as well but a linear combination of the flux and chiral symmetries remains unbroken. A similar symmetry breaking pattern U(1) ⊗ U(1) → U(1) is realized also in Chern-Simons electrodynamics for a particular value of the Chern-Simons coefficient at which the photon becomes massless (anyon superconductor). The pertinent order parameter for the Higgs-Coulomb phase transition in scalar QED is identified with the vev of the magnetic vortex creation operator V( x). We calculate, using weak coupling perturbation theory, the vev and the correlator of V( x) in both phases. This turns out to be equivalent to evaluation of the euclidean QED partition function in the presence of the external current which produces a magnetic monopole (with the contribution of the Dirac string subtracted). In the Higgs phase this vev vanishes in accord with the Wigner-Weyl realization of the flux symmetry. In the Coulomb phase of scalar QED we obtain a nonzero value of the order parameter whereas in the spinor QED it vanishes. This indicates that in the scalar QED the symmetry breaking is of the usual Nambu-Goldstone type while in the spinor QED it is of Kosterlitz-Thouless type.

SUPERCONDUCTIVITY AND SUPERSYMMETRIC QED3

Current theories of high temperature superconductivity are based on the behavior of the ideal (2+1)-dimensional anyon gas at finite density. The anyon gas can be described using fundamental fermionic or bosonic matter in interaction with a topologically massive statistical gauge field. If the renormalized Chern-Simons coefficient at zero density takes the values γR(0)=N/2π, the anyon gas is a superfluid, and if the fundamental matter is electrically charged, it behaves like a superconductor. In this article we analyze an ideal anyon gas composed of two anyonic species, each associated with fundamental matter that has different (fermionic and bosonic) statistics. For supersymmetric values of the masses and couplings, no exotic statistics can occur when the system is in a superconducting state at finite density. However, semionic superconductivity can be achieved when the supersymmetry is very softly broken by a fundamental boson-fermion mass splitting.