New chiral lattice actions of the Boriçi-Creutz type

Abstract

We generalize the Boriçi-Creutz action in such a way that the position of the second zero and the direction which breaks the hypercubic symmetry can be arbitrarily chosen, and the action has still the correct continuum limit. Minimal doubling is guaranteed if the distance between the two zeros does not become too large. Special values of this distance could turn out to be particularly convenient for efficient numerical simulations of minimally doubled fermions.

Mixed action with Borici-Creutz fermions on a staggered sea

“…Because of the broken hypercubic symmetry, the counterterms are necessary for a renormalized theory. The allowed counterterms for the Borici-Creutz action are dimension-4 counterterm c 4 (g 0 )ψΓ µ D µ ψ and dimension-3 counterterm ic 3 (g 0 )ψΓψ (for a discussion of counterterms in the context of minimally doubled fermions see [8]). Then the complete renormalized action, with the gauge interaction turned on, reads…”

“…where,c 3 = c 3 −2, γ µ = Γ−γ µ = Γγ µ Γ and g 0 is the bare coupling parameter. The coefficients of the dimension-3 and 4 counterterms, c 3 and c 4 respectively, have been evaluated in 1-loop lattice perturbation theory [8] and are given by,…”

“…This introduces non-covariant counterterms through quantum corrections. The renormalization properties of the BC fermion at one loop in perturbation theory have been investigated in [7,8]. It was shown that in presence of gauge background with integer-valued topological charge, BC action satisfies the Atiyah-Singer index theorem [9].…”

New actions for minimally doubled fermions and their counterterms

“…It turns out that for the massless Karsten-Wilczek (KW) and Boriçi-Creutz (BC) formulations three counterterms need to be added to the bare action in order to remove the hypercubic-breaking contributions [7,8,9,10]. A consistent renormalized theory can be achieved only for special values of the coefficients of the counterterms, which then have to be appropriately tuned.…”

Mass spectroscopy using Borici–Creutz fermions on 2D lattice

“…The important question is how bad the effects of the symmetry breaking are in a numerical simulation. It was shown that a consistent renormalizable theory for minimally doubled fermion can be constructed by fixing only three counter terms allowed by the symmetry and the counter terms for BC action at one loop in perturbation theory have been evaluated [6,7]. But, till date, sufficient numerical studies of the minimally doubled fermions have not been done.…”