Soft-Collinear Supersymmetry

Abstract

Soft-Collinear Effective Theory (SCET) is a framework for modeling the infrared structure of theories whose long distance behavior is dominated by soft and collinear divergences. This paper demonstrates that SCET can be made compatible with supersymmetry (SUSY). Explicitly, the effective Lagrangian for $\mathcal{N} = 1$ SUSY Yang-Mills is constructed and shown to be a complete description for the infrared of this model. For contrast, we also construct the effective Lagrangian for chiral SUSY theories with Yukawa couplings, specifically the single flavor Wess-Zumino model. Only a subset of the infrared divergences are reproduced by the Lagrangian -- to account for the complete low energy description requires the inclusion of local operators. SCET is formulated by expanding fields along a light-like direction and then subsequently integrating out degrees-of-freedom that are away from the light-cone. Defining the theory with respect to a specific frame obfuscates Lorentz invariance -- given that SUSY is a space-time symmetry, this presents a possible obstruction. The cleanest language with which to expose the congruence between SUSY and SCET requires exploring two novel formalisms: collinear fermions as two-component Weyl spinors, and SCET in light-cone gauge. By expressing SUSY Yang-Mills in "collinear superspace", a slice of superspace derived by integrating out half the fermionic coordinates, the light-cone gauge SUSY SCET theory can be written in terms of superfields. As a byproduct, bootstrapping up to the full theory yields the first algorithmic approach for determining the SUSY Yang-Mills on-shell superspace action. This work paves the way toward discovering the effective theory for the collinear limit of $\mathcal{N} = 4$ SUSY Yang-Mills.