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Register a new userCharge Condensation in QED$_3$ with a Chern-Simons Term
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Introducing a chemical potential in the functional method, we construct the effective action of QED$_3$ with a Chern-Simons term. We examine a possibility that charge condensation $langlepsi^daggerpsi rangle$ remains nonzero at the limit of the zero chemical potential. If it happens, spontaneous magnetization occurs due to the Gauss law constraint which connects the charge condensation to the background magnetic field. It is found that the stable vacuum with nonzero charge condensation is realized only when fermion masses are sent to zero, keeping it lower than the chemical potential. This result suggests that the spontaneous magnetization is closely related to the fermion mass.
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The contribution of nontrivial vacuum (topological) excitations, more specifically vortex configurations of the self-dual Chern-Simons-Higgs model, to the functional partition function is considered. By using a duality transformation, we arrive at a representation of the partition function in terms of which explicit vortex degrees of freedom are coupled to a dual gauge field. By matching the obtained action to a field theory for the vortices, the physical properties of the model in the presence of vortex excitations are then studied. In terms of this field theory for vortices in the self-dual Chern-Simons Higgs model, we determine the location of the critical value for the Chern-Simons parameter below which vortex condensation can happen in the system. The effects of self-energy quantum corrections to the vortex field are also considered.
We study dynamical symmetry breaking in three-dimensional QED with a Chern-Simons (CS) term, considering the screening effect of $N$ flavor fermions. We find a new phase of the vacuum, in which both the fermion mass and a magnetic field are dynamically generated, when the coefficient of the CS term $kappa$ equals $N e^2/4 pi$. The resultant vacuum becomes the finite-density state half-filled by fermions. For $kappa=N e^2/2 pi$, we find the fermion remains massless and only the magnetic field is induced. For $kappa=0$, spontaneous magnetization does not occur and should be regarded as an external field.
The issue intensively claimed in the literature on the generation of a CPT-odd and Lorentz violating Chern-Simons-like term by radiative corrections owing to a CPT violating interaction -- the axial coupling of fermions with a constant vector field $b_m$ -- is mistaken. The presence of massless gauge field triggers IR divergences that might show up from the UV subtractions, therefore, so as to deal with the (actual physical) IR divergences, the Lowenstein-Zimmermann subtraction scheme, in the framework of BPHZL renormalization method, has to be adopted. The proof on the non generation of such a Chern-Simons-like term is done, independent of any kind of regularization scheme, at all orders in perturbation theory.
We extend our recent work on the quasilocal formulation of conserved charges to a theory of gravity containing a gravitational Chern-Simons term. As an application of our formulation, we compute the off-shell potential and quasilocal conserved charges of some black holes in three-dimensional topologically massive gravity. Our formulation for conserved charges reproduces very effectively the well-known expressions on conserved charges and the entropy expression of black holes in the topologically massive gravity.
The radiative induction of the CPT and Lorentz violating Chern-Simons (CS) term is reassessed. The massless and massive models are studied. Special attention is given to the preservation of gauge symmetry at higher orders in the background vector $b_mu$ when radiative corrections are considered. Both the study of the odd and even parity sectors of the complete vacuum polarization tensor at one-loop order and a non-perturbative analysis show that this symmetry must be preserved by the quantum corrections. As a complement we obtain that transversality of the polarization tensor does not fix the value of the coefficient of the induced CS term.
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