### Classification of irreps and invariants of the N-extended Supersymmetric Quantum MechanicsClassification of irreps and invariants of the N-extended Supersymmetric Quantum Mechanics

Access Restriction
Open

 Author Kuznetsova, Z. ♦ Rojas, M. ♦ Toppan, F. Source arXiv.org Content type Text File Format PDF Date of Submission 2005-11-27 Language English
 Subject Domain (in DDC) Computer science, information & general works ♦ Natural sciences & mathematics ♦ Mathematics ♦ Physics Subject Keyword High Energy Physics - Theory ♦ Mathematical Physics ♦ Quantum Physics ♦ math ♦ physics:hep-th ♦ physics:math-ph ♦ physics:quant-ph Abstract We present an algorithmic classification of the irreps of the $N$-extended one-dimensional supersymmetry algebra linearly realized on a finite number of fields. Our work is based on the 1-to-1 \cite{pt} correspondence between Weyl-type Clifford algebras (whose irreps are fully classified) and classes of irreps of the $N$-extended 1D supersymmetry. The complete classification of irreps is presented up to $N\leq 10$. The fields of an irrep are accommodated in $l$ different spin states. N=10 is the minimal value admitting length $l>4$ irreps. The classification of length-4 irreps of the N=12 and {\em real} N=11 extended supersymmetries is also explicitly presented.\par Tensoring irreps allows us to systematically construct manifestly ($N$-extended) supersymmetric multi-linear invariants {\em without} introducing a superspace formalism. Multi-linear invariants can be constructed both for {\em unconstrained} and {\em multi-linearly constrained} fields. A whole class of off-shell invariant actions are produced in association with each irreducible representation. The explicit example of the N=8 off-shell action of the $(1,8,7)$ multiplet is presented.\par Tensoring zero-energy irreps leads us to the notion of the {\em fusion algebra} of the 1D $N$-extended supersymmetric vacua. Description Reference: JHEP0603:098,2006 Educational Use Research Learning Resource Type Article Page Count 52