Dimensional Enhancement via Supersymmetry

TL;DR

This paper develops an algebraic framework to identify which one-dimensional supersymmetric models are shadows of higher-dimensional theories, enabling dimensional enhancement and understanding of gauge invariance in supersymmetric quantum mechanics.

Contribution

It introduces algebraic criteria to determine supersymmetric model shadows and formalizes the concept of 'phantoms' for higher-dimensional gauge invariance within one-dimensional models.

Findings

Reproduces known supersymmetric field theory results using one-dimensional models

Defines criteria for supersymmetric model enhancement to higher dimensions

Introduces 'phantoms' to incorporate gauge invariance in shadow multiplets

Abstract

We explain how the representation theory associated with supersymmetry in diverse dimensions is encoded within the representation theory of supersymmetry in one time-like dimension. This is enabled by algebraic criteria, derived, exhibited, and utilized in this paper, which indicate which subset of one-dimensional supersymmetric models describe "shadows" of higher-dimensional models. This formalism delineates that minority of one-dimensional supersymmetric models which can "enhance" to accommodate extra dimensions. As a consistency test, we use our formalism to reproduce well-known conclusions about supersymmetric field theories using one-dimensional reasoning exclusively. And we introduce the notion of "phantoms" which usefully accommodate higher-dimensional gauge invariance in the context of shadow multiplets in supersymmetric quantum mechanics.