Spontaneous chiral-symmetry breaking in three-dimensional QED with a Chern-Simons term

Abstract

In three-dimensional $ED with a Chern-Simons term we study the phase structure associated with chiral-symmetry breaking in the framework of the Schwinger-Dyson equation. We give detailed analyses on the analytical and numerical solutions for the Schwinger-Dyson equation of the fermion propagator, where the nonlocal gauge-fixing procedure is adopted to avoid wave-function reriormalization for the fermion. In the absence of the Chern-Simons term, there exists a finite critical number of four-component fermion flavors, at which a continuous (infinite-order) chiral phase transition takes place and below which the chiral symmetry is spontaneously broken. In the presence of the Chern-Simons term, we find that the spontaneous chiral-symmetry-breaking transition continues to exist, but the type of phase transition turns into a discontinuous first-order transition. A simple stability argument is given based on the effective potential, whose stationary point gives the solution of the Schwinger-Dyson equation.

Determine the critical fermion flavor in three-dimensional QED using nonlocal gauge

“…At finite temperature QED 3 , there still exists a critical fermion flavor, which will be reduced by the temperature increasing. [24][25][26][27][28] In the nonlocal gauge, [9][10][11][29][30][31][32][33] the gauge parameter ξ is dependent on the momentum or coordinates, while in the usual R ξ gauge, ξ is just a constant. The nonlocal gauge can be transformed into the Landau gauge by the inverse LKFT.…”

Study of Dynamical Chiral Symmetry Breaking in (2 + 1) Dimensional Abelian Higgs Model

“…It has many features similar to quantum chromodynamics (QCD), such as spontaneous chiral symmetry breaking in the massless fermion limit and confinement [1][2][3][4][5][6][7][8][9][10][11][12][13]. Moreover, it is super-renormalizable, so it does not suffer from the ultraviolet divergence which are present in QED 4 .…”

The relation between Pauli and γ representation in QED3 and induced Chern-Simons term

“…When studying DCSB in QED 3 , one has to use four-component fermions with γ matrices [5][6][7][8][9][10][11][12][13][14], since the model with two-component fermions with Pauli matrices does not have chiral properties due to the property of Pauli matrix algebra. On the other hand, Chern-Simons theory has induced many significative studies in QED 3 [15][16][17][18]. Besides introducing Chern-Simons term into the normal QED 3 Lagrangian, it was also found that in QED 3 with two-component fermions a Chern-Simons like term can also be induced from radiative corrections [19][20][21][22][23][24][25] (Appendix A).…”