Abstract
This work covers part of the material presented at the Advanced Summer School in Prague. It is mostly devoted to the structural properties of Extended Supersymmetries in One Dimension. Several results are presented on the classification of linear, irreducible representations realized on a finite number of time-dependent fields. The connections between supersymmetry transformations, Clifford algebras and division algebras are discussed. A manifestly supersymmetric framework for constructing invariants without using the notion of superfields is presented. A few examples of one-dimensional, N-extended, off-shell invariant sigma models are computed. The relation between supersymmetry transformations and graph theory is outlined. The notion of the fusion algebra of irreps tensor products is presented. The relevance of one-dimensional Supersymmetric Quantum Mechanics as a way to extract information on higher dimensional supersymmetric field theories is discussed.
Highlights
ToppanThis work covers part of the material presented at the Advanced Summer School in Prague
Supersymmetric Quantum Mechanics [1] is under intensive development and remarkable new features have been discovered in recent years
It is well known that large N one-dimensional supersymmetric quantum mechanical models are automatically derived [7] from dimensional reduction of higher-dimensional supersymmetric field theories
Summary
This work covers part of the material presented at the Advanced Summer School in Prague. It is mostly devoted to the structural properties of Extended Supersymmetries in One Dimension. Several results are presented on the classification of linear, irreducible representations realized on a finite number of time-dependent fields. The connections between supersymmetry transformations, Clifford algebras and division algebras are discussed. A manifestly supersymmetric framework for constructing invariants without using the notion of superfields is presented. A few examples of one-dimensional, N-extended, off-shell invariant sigma models are computed. The relation between supersymmetry transformations and graph theory is outlined. The notion of the fusion algebra of irreps tensor products is presented. The relevance of one-dimensional Supersymmetric Quantum Mechanics as a way to extract information on higher dimensional supersymmetric field theories is discussed
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