On the Continuum and Lattice Formulations of N=4 D=3 Twisted Super Yang-Mills

TL;DR

This paper develops an off-shell continuum formulation of N=4 D=3 twisted super Yang-Mills using twisted superspace, clarifies its relation to lattice formulations, and identifies the B-type twist as the only lattice-compatible option.

Contribution

It provides a new off-shell continuum formulation of N=4 D=3 twisted super Yang-Mills and clarifies the lattice realization constraints for different topological twists.

Findings

The continuum formulation employs a twisted superspace with eight supercharges.

The lattice formulation corresponds to the B-type twist of N=4 D=3.

Only the B-type twist can be consistently realized on the lattice with gauge covariance.

Abstract

Employing a twisted superspace with eight supercharges, we describe an off-shell formulation of N=4 D=3 twisted super Yang-Mills in the continuum spacetime which underlies the recent proposal of N=4 D=3 twisted super Yang-Mills on a lattice (arXiv:0707.3533[hep-lat]). By a dimensional reduction from the N=2 D=4, we explore the two possible topological twists of N=4 D=3 and then show that the lattice formulation given in arXiv:0707.3533[hep-lat] is essentially categorized as the B-type. We also show that, amongst the two inequivalent twists of N=4 D=3, only the B-type SYM can be realized on the lattice consistently with the Leibniz rule and the gauge covariance on the lattice.