SUSY Jumps Out of Superspace in the Supersymmetric Standard Model

Abstract

The supersymmetric standard model (SSM) appears to be firmly grounded in superspace. For example, it would be natural to assume that all the physically important composite operators can be made by combining superfields and superspace derivatives. But even for the simplest possible, free, massless and unbroken SUSY theory in 3+1 dimensions, this is not true. This paper shows that there is a large set of physically important composite operators in the SSM that require explicit factors of the Grassmann odd `$\theta$' parameters of superspace. These explicitly break superspace invariance. These composite operators will be called `Outfields', because they are intrinsically `outside' of superspace. It is not possible to write the Outfields using only superfields and superspace derivatives. The Outfields can be found in the BRST cohomology space of the theory. The calculation of the BRST cohomology space for these theories is performed in this paper using a spectral sequence analysis, starting with the free massless theory, and then adding interactions, and then masses.

arXiv comment91 pages

References in corpus (1)

• Gauge Invariance in Field Theory and Statistical Physics in Operator Formalism

Cited by in corpus (5)

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• Chiral SUSY Theories with a Suppressed SUSY Charge
• SUSY Invariants from the BRST Cohomology of the SOSO Model
• An Extraordinary Mass Invariant and an Obstruction in a Massive Superspin One Half Model made with a Chiral Dotted Spinor Superfield
• Does SUSY know about the Standard Model?