Domain wall fermions with Majorana couplings

Abstract

We examine the lattice boundary formulation of chiral fermions with either an explicit Majorana mass or a Higgs-Majorana coupling introduced on one of the boundaries. We demonstrate that the low-lying spectrum of the models with an explicit Majorana mass of the order of an inverse lattice spacing is chiral at tree level. Within a mean-field approximation we show that the systems with a strong Higgs-Majorana coupling have a symmetric phase, in which a Majorana mass of the order of an inverse lattice spacing is generated without spontaneous breaking of the gauge symmetry. We argue, however, that the models within such a phase have a chiral spectrum only in terms of the fermions that are singlets under the gauge group. The application of such systems to nonperturbative formulations of supersymmetric and chiral gauge theories is briefly discussed.

Vectorlike gauge theories with almost massless fermions on the lattice

“…In [3,1] we defined the topological charge n top as half the difference between the number of positive and negative eigenvalues of H. This implies 21) confirming the interpretation of the sign of µ as the sign of the physical mass. Similarly, one could treat complex masses, or (in the case of several light flavors) mass matrices.…”

“…Here we wish to present simplified formulae of the type in [1] for the effective actions for the supersymmetric case, both in the truncated models and in the overlap limit. For other work with Majorana fermions see [21].…”

Gauge freedom in chiral gauge theory with vacuum overlap

“…The possible existence of the PMS phase in the waveguide formulation was already argued in the recent proposal of the gauge invariant formulation of the standard model with the invariant four-fermion operators [13]. Quite recently, it was also argued in the system with the Majorana type Yukawa coupling [14]. Our result is suggesting that, in the case of the two-dimensional nonabelian gauge theory, the PMS phase can also exist in the waveguide model with the Dirac type Yukawa coupling.…”

“…It has been one of the most important issues to clarify the dynamical behavior of the gauge freedom and its effect to the fermion spectrum for various proposals of lattice chiral gauge theory [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17]. In this article, we discuss this issue in the context of the vacuum overlap formulation [16].…”

Single Massless Majorana Fermion in the Domain-Wall Formalism

“…The propagator of the fermions in the domain-wall formalism with the Majorana-type coupling has been calculated in Ref. [10]. The one for η can be written as…”