Exact Extended Supersymmetry on a Lattice: Twisted N=2 Super Yang-Mills in Two Dimensions

TL;DR

This paper introduces a lattice formulation for two-dimensional N=2 super Yang-Mills theory that preserves extended supersymmetry exactly, using a novel fermionic link structure and a modified Leibniz rule, with potential extensions to N=4 in four dimensions.

Contribution

It presents a new lattice action that exactly realizes extended supersymmetry, employing a twisted approach with fermionic links and semi-local superfields, and discusses its extension to higher dimensions.

Findings

Supersymmetry is exactly preserved on the lattice.

The lattice uses fermionic links and modified Leibniz rule.

The approach can be extended to N=4 supersymmetry in four dimensions.

Abstract

We propose a lattice action for two dimensional super Yang-Mills theory with a twisted N=2 supersymmetry. The extended supersymmetry is fully and exactly realized on the lattice. The method employed is quite general and its extension to the N=4 supersymmetry in four dimensions is briefly presented. The lattice has a new type of ``fermionic'' links, where odd Grassmann variables, supercharges and fermionic connections sit. The Leibniz rule is preserved on the lattice, although in a modified ``shifted'' form that takes into account the link nature of both derivatives and supercharges. Superfields are semi-local objects and superfield expansion is naturally embedded in the lattice structure. The Dirac-K\"ahler twist generates the extended twisted supersymmetry, turning the multiplicity of species doublers into the multiplicity due to the extended supersymmetry. In this way the balance between bosonic and fermionic degrees of freedom is preserved.