Holonomies of gauge fields in twistor space 7: an electroweak model

Abstract

We consider massive deformation of $U(2)$ gauge bosons in a recently developed holonomy formalism and propose a novel electroweak model. The massive gauge bosons arise from massive deformation of spinor momenta, which implies that the mass generation is implemented by Lorentz symmetry breaking rather than the spontaneous gauge symmetry breaking. Following the notation of the holonomy formalism, we interpret the weak hypercharge of a left-handed fermion doublet as the reciprocal of the Knizhnik-Zamolodchikov (KZ) parameter $\kappa =k+h^{\vee }$ where $k$ is the level number, fixed at $k=1$, and $h^{\vee }$ is the dual Coxeter number for $SU(2{)}_L$. This leads to natural distinction between quarks and leptons in terms of a weight for the representation of $SU(2{)}_L$. Physical operators of the electroweak vector bosons and fermions are defined by use of Grassmann variables. Possible electroweak interactions are then determined by the evaluation of Grassmann integrals. We obtain a generating functional for the electroweak interaction vertices and illustrate how to compute decay rates of the $Z$-boson into a pair of fermions.

23 pages; v2. references updated

References in corpus (7)

• On-shell supersymmetry for massive multiplets
• The Coulomb-branch S-matrix from massless amplitudes
• Twistor-inspired construction of massive quark amplitudes
• Holonomies of gauge fields in twistor space 1: bialgebra, supersymmetry, and gluon amplitudes
• Holonomies of gauge fields in twistor space 4: functional MHV rules and one-loop amplitudes
• Holonomies of gauge fields in twistor space 5: amplitudes of gluons and massive scalars
• Holonomies of gauge fields in twistor space 6: incorporation of massive fermions