geometric representation theory
representation, 2-representation, ∞-representation
Grothendieck group, lambda-ring, symmetric function, formal group
principal bundle, torsor, vector bundle, Atiyah Lie algebroid
Eilenberg-Moore category, algebra over an operad, actegory, crossed module
Be?linson-Bernstein localization?
superalgebra and (synthetic ) supergeometry
A supermultiplet is an irreducible representation of a supersymmetry supergroup or super Lie algebra, decomposed as a direct sum (branching) of irreps of the underlying ordinary group.
For the case of unitary representations of the super Poincaré group, then under the canonical inclusion of the ordinary Poincaré group into the super Poincaré group, the supermultiplets for super-isometries of super Minkowski spacetime decompose into a direct sum of irreducible unitary representations of the Poincaré group. Via the Wigner classification of fundamental particles as irreps of the Poincaré group, this gives a decomposition of supermultiplets into particle species. The particles in this direct sum related by odd supersymmetry transformations are called superpartners.
Similar statements hold for the super anti de Sitter group or superconformal group etc.
By Deligne's theorem on tensor categories the most general regular tensor categories are those spanned by supermultiplets for some supergroup.
Leonardo Castellani, Riccardo D'Auria, Pietro Fré, chapter II.4 in Supergravity and Superstrings - A Geometric Perspective, World Scientific (1991)
Veeravalli Varadarajan, section 5.3 of Unitary representations of super Lie groups, 2006 (pdf)
See also:
Relation to -algebras via pure spinor-formalism:
Last revised on April 5, 2023 at 08:31:34. See the history of this page for a list of all contributions to it.