Lattice supersymmetry with Hopf algebra for the link approach

TL;DR

This paper develops a formalism for lattice supersymmetry by identifying a lattice-deformed superalgebra as a Hopf algebra, incorporating deformed Leibniz rules and statistics, enabling the construction of a braided quantum field theory.

Contribution

It introduces a Hopf algebra framework for lattice supersymmetry, integrating deformed Leibniz rules and statistics into a consistent algebraic structure.

Findings

Superalgebra identified as a Hopf algebra satisfying all axioms.

Deformed Leibniz rules incorporated via coproduct structure.

Constructed perturbative lattice field theory with braided statistics.

Abstract

A formalism of lattice supersymmetry based on a lattice-deformed superalgebra which was originally introduced in the link approach formulation is presented. We propose that the superalgebra can in fact be identified as a Hopf algebra, showing all the Hopf algebra axioms and consistencies are satisfied with explicit formulae. In particular, the "deformed" Leibniz rules proposed in the original link approach are now built in the coproduct structure of the Hopf algebra. Fields in this scheme, as representations of the Hopf algebra, are found to obey a kind of mildly deformed statistics, which is interpreted as a braiding strucutre. We can then construct, at least perturbatively, the corresponding lattice field theory, which has the Hopf algebraic symmetry with the deformed statistics, as an example of braided quantumm field theory formulated by Oeckl.