Representations of Super Yang-Mills Algebras

• Autores: Herscovich Ramoneda, Estanislao Benito
• Año de publicación: 2012
• Idioma: inglés
• Tipo de recurso: artículo
• Materia: Yang-Mills; Orbit Method; Representation Theory; Homology Theory; Lie Superalgebras
• Institución: Consejo Nacional de Investigaciones Científicas y Técnicas

We study in this article the representation theory of a family of super algebras, called the super Yang-Mills algebras, by exploiting the Kirillov orbit method à la Dixmier for nilpotent super Lie algebras. These super algebras are an extension of the so-called Yang-Mills algebras, introduced by A. Connes and M. Dubois-Violette in (Lett Math Phys 61(2):149–158, 2002), and in fact they appear as a “background independent” formulation of supersymmetric gauge theory considered in physics, in a similar way as Yang-Mills algebras do the same for the usual gauge theory. Our main result states that, under certain hypotheses, all Clifford-Weyl super algebras Cliffq (k)⊗ Ap(k), for p ≥ 3, or p = 2 and q ≥ 2, appear as a quotient of all super Yang-Mills algebras, for n ≥ 3 and s ≥ 1. This provides thus a family of representations of the super Yang-Mills algebras.
Fil: Herscovich Ramoneda, Estanislao Benito. Universitat Bielefeld; Alemania. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina