Majorana and Majorana-Weyl fermions in lattice gauge theory

We investigate, analytically and numerically, the fermion determinant of a new action on a (1+1)-dimensional Euclidean lattice. In this formulation the discrete chiral symmetry is preserved and the number of fermion components is a half of that of Kogut-Susskind. In particular, we show that our fermion determinant is real and positive for U(1) gauge group under specific conditions, which correspond to gauge conditions on the infinite lattice. It is also shown that the determi...

This is a pedagogical article which discusses various kinds of fermion fields: Dirac, Majorana and Weyl. The definitions and motivations for introducing each kind of fields is discussed, along with the connections between them. It is pointed out that these definitions have to do with the proper Lorentz group, and not with respect to any discrete symmetry. The relationship of discrete symmetries like charge conjugation and CP, particularly important for Majorana fermions, has ...

Eight Majorana fermions in $d=1+1$ dimensions enjoy a triality that permutes the representation of the $SO(8)$ global symmetry in which the fermions transform. This triality plays an important role in the quantization of the superstring, and in the analysis of interacting topological insulators and the associated phenomenon of symmetric mass generation. The purpose of these notes is to provide an introduction to the triality and its applications, with careful attention paid t...

Can one make a Majorana field theory for fermions starting from the zero mass Weyl theory, then adding a mass term as an interaction? The answer to this question is: yes we can. We can proceed similarly to the case of the Dirac massive field theory. In both cases one can start from the zero mass Weyl theory and then add a mass term as an interacting term of massless particles with a constant (external) field. In both cases the interaction gives rise to a field theory for a fr...

An overlap method for regularizing Majorana--Weyl fermions interacting with gauge fields is presented. A mod(2) index is introduced in relation to the anomalous violation of a discrete global chiral symmetry. Most of the paper is restricted to 2 dimensions but generalizations to 2+8k dimensions should be straightforward.

The construction of CP-invariant lattice chiral gauge theories and the construction of lattice Majorana fermions with chiral Yukawa couplings is subject to topological obstructions. In the present work we suggest lattice extensions of charge and parity transformation for Weyl fermions. This enables us to construct lattice chiral gauge theories that are CP invariant. For the construction of Majorana-Yukawa couplings, we discuss two models with symplectic Majorana fermions: a m...

In recent years a new class of supersymmetric lattice theories have been proposed which retain one or more exact supersymmetries for non-zero lattice spacing. Recently there has been some controversy in the literature concerning whether these theories suffer from a sign problem. In this paper we address this issue by conducting simulations of the N=(2, 2) and N=(8, 8) supersymmetric Yang--Mills theories in two dimensions for the U(N) theories with N=2,3,4, using the new twist...

We discuss fermions for arbitrary dimensions and signature of the metric, with special emphasis on euclidean space. Generalized Majorana spinors are defined for $d=2,3,4,8,9$ mod 8, independently of the signature. These objects permit a consistent analytic continuation of Majorana spinors in Min-kowski space to euclidean signature. Compatibility of charge conjugation with complex conjugation requires for euclidean signature a new complex structure which involves a reflection ...

We analyse stability of almost massless Dirac mode in gauge models with boundary (domain wall) fermions, and consider the possibility of decoupling one of its chiral component by giving it a Majorana mass of the order of the inverse lattice spacing. We argue that the chiral spectrum in such models is always uncharged, so they can be implemented for defining the Weyl fermions only in the real representation of the gauge group, for instance, in SUSY models.

We formulate supersymmetric Euclidean spacetime Ad* lattices whose classical continuum limits are U(N) supersymmetric Yang-Mills theories with sixteen supercharges in d=1,2,3 and 4 dimensions. This family includes the especially interesting N=4 supersymmetry in four dimensions, as well as a Euclidean path integral formulation of Matrix Theory on a one dimensional lattice.