Yang-Mills and Supersymmetry Covariance Must Coexist

TL;DR

This paper emphasizes that in fundamental physics models, especially in 1+1 dimensions, only a formalism that maintains both gauge invariance and supersymmetry simultaneously can ensure the essential properties of these theories.

Contribution

It demonstrates that in 1+1 dimensions, transforming between gauge-covariant and superfield formalisms is impossible, highlighting the necessity of a covariant formalism that preserves both symmetries.

Findings

Transformation between formalisms is elementary in 3+1 dimensions.

In 1+1 dimensions, such transformation is impossible.

Only gauge- and supersymmetry-covariant formalism guarantees both symmetries.

Abstract

Supersymmetry and Yang-Mills type gauge invariance are two of the essential properties of most, and possibly the most important models in fundamental physics. Supersymmetry is nearly trivial to prove in the (traditionally gauge-noncovariant) superfield formalism, whereas the gauge-covariant formalism makes gauge invariance manifest. In 3+1-dimensions, the transformation from one into the other is elementary and essentially unique. By contrast, this transformation turns out to be impossible in the most general 1+1-dimensional case. In fact, only the (manifestly) gauge- and supersymmetry-covariant formalism guarantees both universal gauge-invariance and supersymmetry.