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The simplest Exotic Invariant (E3)

John A. Dixon

TL;DR

This work constructs the simplest Exotic Invariant E3 within the BRS cohomology of a minimal chiral SUSY theory by decomposing the action into A_fields and A_PseudoFields and introducing a Master Equation that enforces SUSY invariance. A concrete invariant I1 is proposed, with its coefficients determined by δ-invariance and cancellations among variations, supported by spectral sequence reasoning. The paper also provides explicit nilpotent BRS transformations for fields and pseudofields and lays out the Master Equation in detail, establishing the framework for systematic, possibly computer-assisted, verification. The contribution offers a concrete, minimal example of an exotic invariant and sets up the machinery for automated algebraic checks in future work (E10), with potential implications for SUSY model-building and cohomological analyses.

Abstract

This paper E3 shows how to construct the simplest Exotic Invariant in the simplest way.

The simplest Exotic Invariant (E3)

TL;DR

This work constructs the simplest Exotic Invariant E3 within the BRS cohomology of a minimal chiral SUSY theory by decomposing the action into A_fields and A_PseudoFields and introducing a Master Equation that enforces SUSY invariance. A concrete invariant I1 is proposed, with its coefficients determined by δ-invariance and cancellations among variations, supported by spectral sequence reasoning. The paper also provides explicit nilpotent BRS transformations for fields and pseudofields and lays out the Master Equation in detail, establishing the framework for systematic, possibly computer-assisted, verification. The contribution offers a concrete, minimal example of an exotic invariant and sets up the machinery for automated algebraic checks in future work (E10), with potential implications for SUSY model-building and cohomological analyses.

Abstract

This paper E3 shows how to construct the simplest Exotic Invariant in the simplest way.
Paper Structure (8 sections, 41 equations)

This paper contains 8 sections, 41 equations.

Table of Contents

  1. Introduction
  2. The Action ${\cal A}$ for the theory with no superpotential
  3. Field parts ${\cal A}_{\rm Fields}$ of the action
  4. PseudoField parts ${\cal A}_{\rm PseudoFields}$ of the action
  5. The Simplest Example
  6. The Master Equation
  7. Tables of the Nilpotent BRS operator $\delta$ these are older I think
  8. Conclusion