Circumnavigating Collinear Superspace

TL;DR

This paper extends collinear superspace formalism to include full $ cal=1$ supersymmetric interactions, introducing novel supermultiplets and vector superfields to model gauge and matter interactions in a simplified, infrared-focused framework.

Contribution

It develops a comprehensive collinear superspace framework for $ cal=1$ theories, including new supermultiplets and gauge structures, enabling construction of supersymmetric models from infrared data.

Findings

Constructed collinear superspace Lagrangians for $ cal=1$ theories.

Introduced novel Grassmann-valued supermultiplets and vector superfields.

Showed all $ cal=1$ theories in 4D can be built from infrared considerations.

Abstract

In this paper, we extend the collinear superspace formalism to include the full range of $\mathcal{N} = 1$ supersymmetric interactions. Building on the effective field theory rules developed in a companion paper - "Navigating Collinear Superspace" - we construct collinear superspace Lagrangians for theories with non-trivial $F$- and $D$-term auxiliary fields. For (massless) Wess-Zumino models, the key ingredient is a novel type of Grassmann-valued supermultiplet whose lowest component is a (non-propagating) fermionic degree of freedom. For gauge theories coupled to charged chiral matter, the key ingredient is a novel type of vector superfield whose lowest component is a non-propagating gauge potential. This unique vector superfield is used to construct a gauge-covariant derivative; while such an object does not appear in the standard full superspace formalism, it is crucial for modeling gauge interactions when the theory is expressed on a collinear slice. This brings us full circle, by showing that all types of $\mathcal{N} = 1$ theories in four dimensions can be constructed in collinear superspace from purely infrared considerations. We speculate that supersymmetric theories with $\mathcal{N} > 1$ could also be implemented using similar collinear superspace constructions.