Majorana and Majorana-Weyl fermions in lattice gauge theory

We revisit 2D $\mathcal{N}=(2,2)$ super Yang-Mills lattice formulation (Sugino model) to investigate its fermion action with two (Majorana) fermion flavors and exact chiral-$U(1)_{R}$ symmetry. We show that the reconcilement of chiral symmetry and absence of further species-doubling originates in the 4D clifford algebra structure of the action, where 2D two flavors are spuriously treated as a single 4D four-spinor with four 4D gamma matrices introduced into kinetic and Wilson...

The main purpose of this work is to show that massless Dirac equation formulated for non-interacting Majorana-Weyl spinors in higher dimensions, particularly in D=1+9 and D=5+5, can lead to an interpretation of massive Majorana and Dirac spinors in D=1+3. By adopting suitable representations of the Dirac matrices in higher dimensions, we pursue the investigation of which higher dimensional space-times and which mass-shell relation concerning massless Dirac equations in higher...

We develop a systematic method to derive the Majorana representation of the Dirac equation in (1+3)-dimensions. We compare with similar approach in (2+2)-dimensions . We argue that our formalism can be useful to have a better understanding of possible Majorana fermions.

We discuss the motivations, difficulties and progress in the study of supersymmetric lattice gauge theories focusing in particular on ${\cal N}=1$ and ${\cal N}=4$ super Yang-Mills in four dimensions. Brief reviews of the corresponding lattice formalisms are given and current results are presented and discussed. We conclude with a summary of the main aspects of current work and prospects for the future.

Recently, two solutions have been proposed to the long standing problem of $\mathcal{CP}$-symmetry on the lattice, which is particularly evident when considering the construction of chiral gauge theories. The first, based on a lattice modification of $\mathcal{CP}$ 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 gene...

In general, the relativistic wave equation considered to mathematically describe the so-called Majorana particle is the Dirac equation with a real Lorentz scalar potential plus the so-called Majorana condition. Certainly, depending on the representation that one uses, the resulting differential equation changes. It could be a real or a complex system of coupled equations, or it could even be a single complex equation for a single component of the entire wave function. Any of ...

Certain classes of supersymmetric gauge theories, including the well known N=4 supersymmetric Yang-Mills theory, that takes part in the AdS/CFT correspondence, can be formulated on a Euclidean spacetime lattice using the techniques of exact lattice supersymmetry. Great ideas such as topological field theories, Dirac-Kaehler fermions, geometric discretization all come together to create supersymmetric lattice theories that are gauge-invariant, doubler free, local and exact sup...

Starting from the Ginsparg-Wilson relation, a general construction of chiral gauge theories on the lattice is described. Local and global anomalies are easily discussed in this framework and a closed expression for the effective action can be obtained. Particular attention is paid to the non-abelian gauge anomaly, which is shown to be related to a local topological field on the lattice representing the Chern character in 4+2 dimensions.

We present an efficient, covariant, graph-based method to integrate superfields over fermionic spaces of high dimensionality. We illustrate this method with the computation of the most general sixteen-dimensional Majorana-Weyl integral in ten dimensions. Our method has applications to the construction of higher-derivative supergravity actions as well as the computation of string and membrane vertex operator correlators.

Recently there has been some controversy in the literature concerning the existence of a fermion sign problem in the $\mathcal{N}=(2,2)$ supersymmetric Yang--Mills (SYM) theories on the lattice. In this work, we address this issue by conducting Monte Carlo simulations not only for $\mathcal{N}=(2,2)$ but also for $\mathcal{N}=(8,8)$ SYM in two dimensions for the U(N) theories with N=2, using the new ideas derived from topological twisting followed by geometric discretization....