Fermionic symmetry in Ichimatsu-decomposed lattice models

Abstract

We present the lattice models with exact fermionic symmetries relating fermions and link variables. The plaquettes are distributed in an Ichimatsu pattern (chequered). We explain this peculiar structure allows us to have a translation in the algebra of the fermionic symmetries.

Vacuum structure of the Ichimatsu-decomposed lattice models

“…The lattice realization of super Yang-Mills theory has been considered very difficult though highly desirable as a non-perturbative formulation [1,2]. In our previous work and talk [3,4], we reported the presence of exact fermionic symmetries on the 'Ichimatsu' lattice, a novel lattice. If the symmetries survive in the continuum limit, they would be related to a supersymmetry if not to the BRS symmetry.…”

“…12640259 and 13135209 from the Japan Society for the Promotion of Science. matsu' pattern [3,4]. The fields of the Ichimatsu lattice theory are link variables, U n,µ , as the gauge field, and a real staggered fermion, ξ n , as the fermion field.…”