On the Irreps of the N-Extended Supersymmetric Quantum Mechanics and Their Fusion Graphs

TL;DR

This paper reviews the classification of irreducible representations in N-extended supersymmetric quantum mechanics, confirms previous results, and introduces a graphical fusion algebra, including explicit N=2 graphs.

Contribution

It provides a detailed classification of irreducible representations and introduces a graphical presentation of the fusion algebra, including the first explicit N=2 graphs.

Findings

Confirmed the agreement of classification results with previous work

Introduced a graphical presentation of the fusion algebra

Presented explicit N=2 fusion graphs for the first time

Abstract

In this talk we review the classification of the irreducible representations of the algebra of the N-extended one-dimensional supersymmetric quantum mechanics presented in hep-th/0511274. We answer some issues raised in hep-th/0611060, proving the agreement of the results here contained with those in hep-th/0511274. We further show that the fusion algebra of the 1D N-extended supersymmetric vacua introduced in hep-th/0511274 admits a graphical presentation. The N=2 graphs are here explicitly presented for the first time.