Twisted Superspace on a Lattice

TL;DR

This paper introduces a novel lattice formulation that preserves exact twisted supersymmetry using a twisted superspace approach, demonstrating explicit models and a unique three-dimensional lattice structure.

Contribution

It develops a new lattice formalism with exact twisted supersymmetry by incorporating noncommutativity, extending twisted superspace to lattice models.

Findings

Explicit N=2 twisted supersymmetry invariant models in 2D

Introduction of mild noncommutativity to preserve Leibniz rule

Discovery of a three-dimensional lattice structure for superspace

Abstract

We propose a new formulation which realizes exact twisted supersymmetry for all the supercharges on a lattice by twisted superspace formalism. We show explicit examples of N=2 twisted supersymmetry invariant BF and Wess-Zumino models in two dimensions. We introduce mild lattice noncommutativity to preserve Leibniz rule on the lattice. The formulation is based on the twisted superspace formalism for N=D=2 supersymmetry which was proposed recently. From the consistency condition of the noncommutativity of superspace, we find an unexpected three-dimensional lattice structure which may reduce into two dimensional lattice where the superspace describes semilocally scattered fermions and bosons within a double size square lattice.