Off-shell invariant super Yang-Mills with gauged central charges for N=D=2 and N=D=4: "Do we need a constraint ?"

TL;DR

This paper explores the construction of off-shell invariant super Yang-Mills theories with central charges in 2D and 4D, examining the necessity of constraints for off-shell closure and invariance.

Contribution

It derives off-shell invariant twisted super Yang-Mills algebras with central charges in 2D and 4D, analyzing the role of constraints in achieving off-shell invariance.

Findings

Off-shell N=2 algebra in 2D can be obtained with or without constraints.

In 4D, off-shell N=4 algebra always requires a constraint.

The super connection ansatz formalism effectively constructs these algebras.

Abstract

We investigate to derive off-shell invariant twisted super Yang-Mills for N=2 in 2-dimensions and N=4 in 4-dimensions with a central charge by super connection ansatz formalism. We find off-shell invariant N=2 algebra with and without an extra constraint in 2-dimensions. On the other hand in 4-dimensions we find off-shell invariant N=4 twisted SUSY algebra including one central charge always with a constraint.