An Alternative Lattice Field Theory Formulation Inspired by Lattice Supersymmetry -Summary of the Formulation-

TL;DR

This paper introduces a novel lattice field theory formulation that addresses key challenges in implementing exact supersymmetry, utilizing a star product to recover the Leibniz rule and avoid fermion doubling, with a framework that approaches continuum locality.

Contribution

It presents a new lattice formulation with a star product that restores the Leibniz rule and avoids fermion doubling, applicable to supersymmetric and non-supersymmetric theories.

Findings

Star product recovers Leibniz rule on the lattice.

Fermion doubling problem is avoided.

Locality is exponentially recovered in the continuum limit.

Abstract

We propose a lattice field theory formulation which overcomes some fundamental difficulties in realizing exact supersymmetry on the lattice. The Leibniz rule for the difference operator can be recovered by defining a new product on the lattice, the star product, and the chiral fermion species doublers degrees of freedom can be avoided consistently. This framework is general enough to formulate non-supersymmetric lattice field theory without chiral fermion problem. This lattice formulation has a nonlocal nature and is essentially equivalent to the corresponding continuum theory. We can show that the locality of the star product is recovered exponentially in the continuum limit. Possible regularization procedures are proposed.The associativity of the product and the lattice translational invariance of the formulation will be discussed.