Chiral Gauge Symmetry Research Articles

The breaking of chiral gauge symmetry

We consider the possibility that the lack of a chiral gauge symmetry-preserving regulator is signaling a genuine quantum effect which breaks the chiral gauge symmetry and generates mass for the gauge bosons. A nonperturbative analysis of an SU(3) C×SU(2) L×U(1) Y model regularized on a lattice is presented. Although both SU(2) L and U(1) Y symmetries in this model are broken in the regularized action, SU(3) C×U(1) Q symmetry can be maintained throughout the calculations. Using a hopping parameter expansion, the effective action for the gauge bosons is derived. Mass terms for the gauge bosons are generated, and the mass ratio of the gauge bosons is discussed.

String theory in four dimensions with three families of chiral fermions and standard gauge symmetry.

A heterotic string theory in four dimensions is constructed by compactifying the ${\mathrm{E}}_{8}$\ifmmode\times\else\texttimes\fi{}${\mathrm{E}}_{8}^{\mathcal{'}}$ heterotic strings from 26 to 4 dimensions via a manifold ${T}^{22}$/G. The theory is modular invariant. In the low-energy limit, there are three families of chiral fermions with exactly the same quantum numbers as in the standard SU(3${)}_{C}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{L}$\ifmmode\times\else\texttimes\fi{}U(1) model. They couple to gravity and gauge fields with the gauge symmetry SU(3${)}_{F}$\ifmmode\times\else\texttimes\fi{}SU(3${)}_{C}$\ifmmode\times\else\texttimes\fi{}SU(2${)}_{L}$\ifmmode\times\else\texttimes\fi{}U(1 ${)}^{3}$. The ${\mathrm{E}}_{8}^{\mathcal{'}}$ is broken down to SU(3)' \ifmmode\times\else\texttimes\fi{}SU(4)'\ifmmode\times\else\texttimes\fi{}U(1)${\mathcal{'}}^{3}$. The SU(4)' group can play the role of the technicolor group to break the SU(2${)}_{L}$ \ifmmode\times\else\texttimes\fi{}U(1${)}^{3}$ symmetry.

Chiral gauge symmetry without anomalies

The Ward identities derived by use of chiral gauge symmetry, when examined in a perturbation expansion using Lagrangian field theory, are found to contain the Adler-Bell-Jackiw-Schwinger anomalies. The cause of this shortcoming is examined, and the result is that when one uses a formulation of field theory in which only fields already renormalized are introduced these anomalies disappear completely. The specific cases examined here are massless two-dimensional electrodynamics with a vector coupling and massless four-dimensional electrodynamics with an axial-vector coupling. In the first example, it is also found that the polarization tensor disappears in second order, and does not exhibit a pole at zero momentum transfer that would cause the vector field to generate a mass spontaneously.