A Ginsparg-Wilson approach to lattice CP symmetry, Weyl and Majoranna fermions, and the Higgs mechanism

Abstract

Recently, two solutions have been proposed to the long standing problem of $\mathcal{C}\mathcal{P}$-symmetry on the lattice, which is particularly evident when considering the construction of chiral gauge theories. The first, based on a lattice modification of $\mathcal{C}\mathcal{P}$ was presented by Igarashi and Pawlowski; the second by myself using the renormalisation group and Ginsparg-Wilson relation. In this work, I combine the two approaches and show that they are each part of a more general framework related to an underlying renormalisation group. I continue by formulating Weyl and Majorana fermions on the lattice, and discussing applications to the fermion propagator in the presence of the Higgs field.

35 pages; v3 some major corrections

References in corpus (9)

• Lower Higgs boson mass bounds from a chirally invariant lattice Higgs-Yukawa model with overlap fermions
• Low-lying Wilson Dirac operator eigenvector mixing in dynamical overlap Hybrid Monte-Carlo
• New overlap construction of Weyl fermions
• A renormalisation group derivation of the overlap formulation
• Symmetries of Ginsparg-Wilson Chiral Fermions
• Majorana fermions and CP-invariance of chiral gauge theories on the lattice
• New solutions to the Ginsparg-Wilson equation
• On Gauged Renormalisation Group Transformations of Lattice Fermions
• Remarks on left-handed lattice fermions

Cited by in corpus (3)

• A further extension to the group of Ginsparg-Wilson (overlap) chiral symmetries
• A Ginsparg-Wilson approach to lattice $\mathcal{C}\mathcal{P}$ symmetry
• The conserved axial current in the presence of multiple chiral symmetries