Introduction to supersymmetric spin networks

Abstract

In this paper we give a general introduction to supersymmetric spin networks. Its construction has a direct interpretation in context of the representation theory of the superalgebra. In particular we analyze a special kind of spin networks with superalgebra $Osp(1|2n)$. It turns out that the set of corresponding spin network states forms an orthogonal basis of the Hilbert space $\cal L\mit^2(\cal A\mit/\cal G)$, and this argument holds even in the q-deformed case. The $Osp(n|2)$ spin networks are also discussed briefly. We expect they could provide useful techniques to quantum supergravity and gauge field theories from the point of non-perturbative view.

27 pages, 16 eps figures. Based on the talk given at Marcel Grossmann Meeting IX in Rome

References in corpus (5)

• Supersymmetric Spin Networks and Quantum Supergravity
• The many faces of OSp(1|32)
• Holographic Formulation of Quantum Supergravity
• Eleven dimensional supergravity as a constrained topological field theory
• Abelian BF-Theory and Spherically Symmetric Electromagnetism

Cited by in corpus (2)

• Super-Group Field Cosmology
• N=2 supersymmetric spin foams in three dimensions