Matrix formulation of superspace on 1D lattice with two supercharges

TL;DR

This paper presents a matrix-based formulation of a supersymmetric theory with two supercharges on a one-dimensional lattice, ensuring exact supersymmetry and unique action construction, with implications for lattice supersymmetry studies.

Contribution

It introduces a matrix representation for superfields that allows for an exact, unambiguous formulation of supersymmetry on a 1D lattice with two supercharges.

Findings

Supersymmetry transformations are uniquely defined without ambiguities.

The action is uniquely constructed and invariant under all supercharges.

Modified Ward identities hold exactly at tree level.

Abstract

Following the approach developed by some of the authors in recent papers and using a matrix representation for the superfields, we formulate an exact supersymmetric theory with two supercharges on a one dimensional lattice. In the superfield formalism supersymmetry transformations are uniquely defined and do not suffer of the ambiguities recently pointed out by some authors. The action can be written in a unique way and it is invariant under all supercharges. A modified Leibniz rule applies when supercharges act on a superfield product and the corresponding Ward identities take a modified form but hold exactly at least at the tree level, while their validity in presence of radiative corrections is still an open problem and is not considered here.