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Soft-collinear supersymmetry. (English) Zbl 1377.81100

Summary: 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 super-symmetry (SUSY). Explicitly, the effective Lagrangian for \(\mathcal{N}=1 \) SUSY Yang-Mills is cconstructed 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 be-tween 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.

MSC:

81T13 Yang-Mills and other gauge theories in quantum field theory
81T60 Supersymmetric field theories in quantum mechanics

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