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Register a new userCompetition and duality correspondence between chiral and superconducting channels in (2+1)-dimensional four-fermion models with fermion number and chiral chemical potentials
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In this paper the duality correspondence between fermion-antifermion and difermion interaction channels is established in two (2+1)-dimensional Gross-Neveu type models with a fermion number chemical potential $mu$ and a chiral chemical potential $mu_5$. The role and influence of this property on the phase structure of the models are investigated. In particular, it is shown that the chemical potential $mu_5$ promotes the appearance of dynamical chiral symmetry breaking, whereas the chemical potential $mu$ contributes to the emergence of superconductivity.
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We investigate the possibility of spatially homogeneous and inhomogeneous chiral fermion-antifermion condensation and superconducting fermion-fermion pairing in the (1+1)-dimensional model by Chodos {it et al.} [ Phys. Rev. D 61, 045011 (2000)] generalized to continuous chiral invariance. The consideration is performed at nonzero values of temperature $T$, electric charge chemical potential $mu$ and chiral charge chemical potential $mu_5$. It is shown that at $G_1<G_2$, where $G_1$ and $G_2$ are the coupling constants in the fermion-antifermion and fermion-fermion channels, the $(mu,mu_5)$-phase structure of the model is in a one-to-one correspondence with the phase structure at $G_1>G_2$ (called duality correspondence). Under the duality transformation the (inhomogeneous) chiral symmetry breaking (CSB) phase is mapped into the (inhomogeneous) superconducting (SC) phase and vice versa. If $G_1=G_2$, then the phase structure of the model is self-dual. Nevertheless, the degeneracy between the CSB and SC phases is possible in this case only when there is a spatial inhomogeneity of condensates.
We show that the presence of a magnetic monopole in position space gives rise to a violation of the fermion number conservation in chiral matter. Using the chiral kinetic theory, we derive a model-independent expression of such a violation in nonequilibrium many-body systems of chiral fermions. In local thermal equilibrium at finite temperature and chemical potential, in particular, this violation is proportional to the chemical potential with a topologically quantized coefficient. These consequences are due to the interplay between the Dirac monopole in position space and the Berry monopole in momentum space. Our mechanism can be applied to study the roles of magnetic monopoles in the nonequilibrium evolution of the early Universe.
In this paper we investigate the phase structure of a (1+1)-dimensional schematic quark model with four-quark interaction and in the presence of baryon ($mu_B$), isospin ($mu_I$) and chiral isospin ($mu_{I5}$) chemical potentials. It is established that in the large-$N_c$ limit ($N_c$ is the number of colored quarks) there exists a duality correspondence between the chiral symmetry breaking phase and the charged pion condensation (PC) one. The role and influence of this property on the phase structure of the model are studied. Moreover, it is shown that the chemical potential $mu_{I5}$ promotes the appearance of the charged PC phase with nonzero baryon density.
Within the scenario of chiral freedom we compute the quark and lepton masses of the first two generations in terms of their chiral couplings. This allows us to make a rough estimate of the size of the chiral couplings, narrowing down the uncertainty in the chiron contribution to low energy observables, like the anomalous magnetic moment of the muon. We also extract information about the chiron mass which determines the size of possible chiron effects at the LHC.
We study the problem of decoupling fermion fields in 1+1 and 2+1 dimensions, in interaction with a gauge field, by performing local transformations of the fermions in the functional integral. This could always be done if singular (large) gauge transformations were allowed, since any gauge field configuration may be represented as a singular pure gauge field. However, the effect of a singular gauge transformation of the fermions is equivalent to the one of a regular transformation with a non-trivial action on the spinorial indices. For example, in the two dimensional case, singular gauge transformations lead naturally to chiral transformations, and hence to the usual decoupling mechanism based on Fujikawa Jacobians. In 2+1 dimensions, using the same procedure, different transformations emerge, which also give rise to Fujikawa Jacobians. We apply this idea to obtain the v.e.v of the fermionic current in a background field, in terms of the Jacobian for an infinitesimal decoupling transformation, finding the parity violating result.
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