Maxwell-Chern-Simons scalar electrodynamics at two loops (original) (raw)

Spontaneous symmetry breaking at two loop in 3-d massless scalar electrodynamics

Physics Letters B, 1996

In three dimensional Maxwell-Chern-Simons massless scalar electrodynamics with φ 6 coupling, the U (1) symmetry is spontaneously broken at two loop order regardless of the presence or absence of the Maxwell term. Dimensional transmutation takes place in pure Chern-Simons scalar electrodynamics. The beta function for the φ 6 coupling is independent of gauge couplings. 1

Two-loop analysis of non-Abelian Chern-Simons theory

Physical Review D, 1992

Perturbative renormalization of a non-Abelian Chern-Simons gauge theory is examined. It is demonstrated by explicit calculation that, in the pure Chern-Simons theory, the beta-function for the coefficient of the Chern-Simons term vanishes to three loop order. Both dimensional regularization and regularization by introducing a conventional Yang-Mills component in the action are used. It is shown that dimensional regularization is not gauge invariant at two loops. A variant of this procedure, similar to regularization by dimensional reduction used in supersymmetric field theories is shown to obey the Slavnov-Taylor identity to two loops and gives no renormalization of the Chern-Simons term. Regularization with Yang-Mills term yields a finite integer-valued renormalization of the coefficient of the Chern-Simons term at one loop, and we conjecture no renormalization at higher order. We also examine the renormalization of Chern-Simons theory coupled to matter. We show that in the non-abelian case the Chern-Simons gauge field as well as the matter fields require infinite renormalization at two loops and therefore obtain nontrivial anomalous dimensions. We show that the beta function for the gauge coupling constant is zero to two-loop order, consistent with the topological quantization condition for this constant.

Loop representation of charged particles interacting with Maxwell and Chern-Simons fields

Physical Review D, 2002

The loop representation formulation of non-relativistic particles coupled with abelian gauge fields is studied. Both Maxwell and Chern-Simons interactions are separately considered. It is found that the loop-space formulations of these models share significant similarities, although in the Chern-Simons case there exists an unitary transformation that allows to remove the degrees of freedom associated with the paths. The existence of this transformation, which allows to make contact with the anyonic interpretation of the model, is subjected to the fact that the charge of the particles be quantized. On the other hand, in the Maxwell case, we find that charge quantization is necessary in order to the geometric representation be consistent.

Spontaneous symmetry breaking and the renormalization of the Chern-Simons term

Physics Letters B, 1995

We calculate the one-loop perturbative correction to the coefficient of the Chern-Simons term in non-abelian gauge theory in the presence of Higgs fields, with a variety of symmetry-breaking structures. In the case of a residual U (1) symmetry, radiative corrections do not change the coefficient of the Chern-Simons term. In the case of an unbroken non-abelian subgroup, the coefficient of the relevant Chern-Simons term (suitably normalized) attains an integral correction, as required for consistency of the quantum theory. Interestingly, this coefficient arises purely from the unbroken non-abelian sector in question; the orthogonal sector makes no contribution. This implies that the coefficient of the Chern-Simons term is a discontinuous function over the phase diagram of the theory. * permanent address:

Off-shell Green functions at one-loop level in Maxwell-Chern-Simons quantum electrodynamics

We derive the off-shell photon propagator and fermion-photon vertex at one-loop level in Maxwell-Chern-Simons quantum electrodynamics in arbitrary covariant gauge, using four-component spinors with parity-even and parity-odd mass terms for both fermions and photons. We present our results using a basis of two, three and four point integrals, some of them not known previously in the literature. These integrals are evaluated in arbitrary space-time dimensions so that we reproduce results derived earlier under certain limits.

Renormalization group and conformal symmetry breaking in the Chern-Simons theory coupled to matter

Physical Review D, 2010

The three-dimensional Abelian Chern-Simons theory coupled to a scalar and a fermionic field of arbitrary charge is considered in order to study conformal symmetry breakdown and the effective potential stability. We present an improved effective potential computation based on two-loop calculations and the renormalization group equation: the later allows us to sum up series of terms in the effective potential where the power of the logarithms are one, two and three units smaller than the total power of coupling constants (i.e., leading, next-to-leading and next-to-next-to-leading logarithms). For the sake of this calculation we determined the beta function of the fermionfermion-scalar-scalar interaction and the anomalous dimension of the scalar field. We shown that the improved effective potential provides a much more precise determination of the properties of the theory in the broken phase, compared to the standard effective potential obtained directly from the loop calculations. This happens because the region of the parameter space where dynamical symmetry breaking occurs is drastically reduced by the improvement discussed here.

Renormalization of Two-Dimensional Massless Quantum Electrodynamics

1998

The Schwinger model, when quantized in a gauge non-invariant way exhibits a dependence on a parameter a (the Jackiw-Rajaraman parameter), in a way which is analogous to the case involving chiral fermions (the chiral Schwinger model). For all values of a 6= 1, there are divergences in the fermionic Green’s functions. We study the renormalization of these divergences in both models to one loop level, defining it in a consistent and semi-perturbative sense that we propose in this paper.

On the non-renormalization properties of gauge theories with a Chern-Simons term

Journal of High Energy Physics, 1998

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 theory. From this we deduce the vanishing of the β-function associated to the Chern-Simons coupling constant and the full finiteness in the case of the Yang-Mills Chern-Simons theory. The main ingredient in the proof of the latter property is the noninvariance of the Chern-Simons form under the gauge transformations. Our results hold for the three-dimensional Chern-Simons model in a general Riemannian manifold.