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The EP Model and its Completion Terms (E4)

J. A. Dixon

TL;DR

The paper develops a minimal supersymmetric EP model with two chiral electron supermultiplets $\\widehat{E}$ and $\\widehat{P}$, including a mass term that imposes a constraint on the Exotic Invariant. It constructs the action $\\mathcal{A}$ as a sum of a Fields and PseudoFields sector, then defines the Exotic Invariant as $\\mathcal{A}_{\\rm X}=\\mathcal{A}_{\\rm X,E}-\\mathcal{A}_{\\rm X,P}$ with coefficients $b_i$ fixed by enforcing $\\delta\\mathcal{A}_{\\rm X}=0$ via the Master Equation in the nilpotent BRST framework; the two-term EI structure arises from the superpotential and a spectral-sequence constraint, with the sign choice ensuring cancellation between $E$ and $P$ contributions. The author proposes a Completed action $\\mathcal{A}_{\\rm Completed}$ that adds Completion Terms ($g\\mathcal{A}_{\\rm X}$, higher-order $\\mathcal{A}_{\\rm X,2}$ and mixed pieces) and conjectures it satisfies the Master Equation, laying groundwork for the Exotic Model XM in $E6$ and guiding subsequent gauge-extended analyses. A central contribution is the explicit decoration of the invariants with fixed coefficients and the systematic BRST- and spectral-sequence-driven approach, together with a clear computational plan (E10) to verify and finalize the completion structure.

Abstract

Here we present the simple example of an Exotic Invariant with just two chiral electron supermultiplets E and P. In this example we include a mass term, and that means that there is a constraint on the Exotic Invariant. The constraint is easily solved for this simple case. Here we also exhibit a simple conjecture for the Completion Terms. This simple example is very useful, because the constraint that arises in the case of the Exotic Model, presented in E6, is just as easy to solve, and the Completion Terms there are also very similar to those here. So this simple EP model is very useful for understanding the Exotic Model, which is what results from adding an Exotic Invariant to the rather complicated Supersymmetric Standard Model.

The EP Model and its Completion Terms (E4)

TL;DR

The paper develops a minimal supersymmetric EP model with two chiral electron supermultiplets and , including a mass term that imposes a constraint on the Exotic Invariant. It constructs the action as a sum of a Fields and PseudoFields sector, then defines the Exotic Invariant as with coefficients fixed by enforcing via the Master Equation in the nilpotent BRST framework; the two-term EI structure arises from the superpotential and a spectral-sequence constraint, with the sign choice ensuring cancellation between and contributions. The author proposes a Completed action that adds Completion Terms (, higher-order and mixed pieces) and conjectures it satisfies the Master Equation, laying groundwork for the Exotic Model XM in and guiding subsequent gauge-extended analyses. A central contribution is the explicit decoration of the invariants with fixed coefficients and the systematic BRST- and spectral-sequence-driven approach, together with a clear computational plan (E10) to verify and finalize the completion structure.

Abstract

Here we present the simple example of an Exotic Invariant with just two chiral electron supermultiplets E and P. In this example we include a mass term, and that means that there is a constraint on the Exotic Invariant. The constraint is easily solved for this simple case. Here we also exhibit a simple conjecture for the Completion Terms. This simple example is very useful, because the constraint that arises in the case of the Exotic Model, presented in E6, is just as easy to solve, and the Completion Terms there are also very similar to those here. So this simple EP model is very useful for understanding the Exotic Model, which is what results from adding an Exotic Invariant to the rather complicated Supersymmetric Standard Model.
Paper Structure (10 sections, 50 equations)

This paper contains 10 sections, 50 equations.

Table of Contents

  1. Introduction
  2. The Action ${\cal A}$ for this theory
  3. Field parts ${\cal A}_{\rm Fields}$ of the action
  4. PseudoField parts ${\cal A}_{\rm PseudoFields}$ of the action
  5. The details of the Exotic Invariant for this EP model
  6. The coefficients $b_i, i =1\cdots 11$ in the exotic invariant ${\cal A}_{\rm X}$
  7. The Master Equation
  8. Tables of the Nilpotent BRS operator $\delta$
  9. Completion of the action that includes the exotic invariant ${\cal A}_{X}$: the completed action ${\cal A}_{\rm Completed}$
  10. Conclusion