Golden Ratio Controlled Chaos in Supersymmetric Dynamics

TL;DR

This paper constructs supersymmetric Lagrangians for a specific N=3 supermultiplet, revealing a parameter space where oscillatory responses are influenced by the golden ratio, and demonstrates possible extensions to N=4 supersymmetry.

Contribution

It introduces new supersymmetric Lagrangians for the N=3 supermultiplet and explores their parameter space, including golden ratio-controlled oscillations and supersymmetry extensions.

Findings

Lagrangians exhibit oscillatory responses influenced by the golden ratio.

All Lagrangians admit an N=3 to N=4 supersymmetry extension.

Some Lagrangians allow two inequivalent N=4 extensions.

Abstract

We construct supersymmetric Lagrangians for the recently constructed off-shell worldline N=3 supermultiplet $Y_I/(i D_I X)$ for I=1,2,3, where $Y_I$ and $X$ are standard, Salam-Strathdee superfields: $Y_I$ fermionic and $X$ bosonic. Already the Lagrangian bilinear in component fields exhibits a total of thirteen free parameters, seven of which specify Zeeman-like coupling to external (magnetic) fluxes. All but special subsets of this parameter space describe aperiodic oscillatory response, some of which are controlled by the "golden ratio," $\varphi\approx1.61803$. We also show that all of these Lagrangians admit an $N=3\to 4$ supersymmetry extension, while a subset admits two inequivalent such extensions.