Irreps and Off-shell Invariant Actions of the N-extended Supersymmetric Quantum Mechanics

Abstract

The complete classification of the irreducible representations of the N-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields is presented. Off-shell invariant actions of one-dimensional supersymmetric sigma models are constructed. The role of both Clifford algebras and the Cayley-Dickson's doublings of algebras in association with the N-extended supersymmetries is discussed. We prove in specific examples that the octonionic structure constants enter the N=8 invariant actions as coupling constants. We further explain how to relate one-dimensional supersymmetric quantum mechanical systems to the dimensional reduction of higher-dimensional supersymmetric theories.

16 pages. Talk given at the Fifth International Conference on Mathematical Methods in Physics IC2006, April 24-28 2006, CBPF, Rio de Janeiro, Brazil

Cited by in corpus (8)

• Hierarchy of N=8 Mechanics Models
• New Model of N=8 Superconformal Mechanics
• Relating Doubly-Even Error-Correcting Codes, Graphs, and Irreducible Representations of N-Extended Supersymmetry
• Critical scaling dimension of D-module representations of N=4,7,8 Superconformal Algebras and constraints on Superconformal Mechanics
• The Common Origin of Linear and Nonlinear Chiral Multiplets in N=4 Mechanics
• Superfield Formulation of Nonlinear N=4 Supermultiplets
• Pure and entangled N=4 linear supermultiplets and their one-dimensional sigma-models
• Properties of HYMNs in Examples of Four-Color, Five-Color, and Six-Color Adinkras