Exact Lattice Supersymmetry at Large N

TL;DR

This paper introduces a new lattice formulation of extended supersymmetry using a non-commutative product, demonstrating exact supersymmetry protection at large N through one-loop quantum correction calculations.

Contribution

It presents a novel non-commutative product approach to formulate exact lattice supersymmetry for extended theories, validated by explicit quantum correction calculations.

Findings

Mass and coupling constants are protected from radiative corrections at non-zero lattice spacing.

Exact lattice supersymmetry is realized in the large-N limit.

Quantum corrections are computed within a lattice superfield framework.

Abstract

Employing a novel type of non-commutative product in the Dirac-Kahler twisted superspace on a lattice, we formulate a field theoretically rigid framework of extended supersymmetry on a lattice. As a first example of this treatment, we calculate one-loop (in some cases any loops) quantum corrections for a twisted Wess-Zumino model with N \times N hermitian matrix superfields on a two dimensional lattice. The calculations are entirely given in a lattice superfield framework. We report that the mass and the coupling constant are exactly protected from the radiative corrections at non-zero lattice spacing as far as the planar diagrams are concerned, which implies the realization of exact lattice supersymmetry w.r.t. all the supercharges in the large-N limit.