Super tensor models, super fuzzy spaces and super n-ary transformations

Abstract

By extending the algebraic description of the bosonic rank-three tensor models, a general framework for super rank-three tensor models and correspondence to super fuzzy spaces is proposed. The corresponding super fuzzy spaces must satisfy a certain cyclicity condition on the algebras of functions on them. Due to the cyclicity condition, the symmetry of the super rank-three tensor models are represented by super n-ary transformations. The Leibnitz rules and the fundamental identities for the super n-ary transformations are discussed from the perspective of the symmetry of the algebra of a fuzzy space. It is shown that the super n-ary transformations of finite orders which conserve the algebra of a fuzzy space form a finite closed n-ary super Lie algebra. Super rank-three tensor models would be of physical interest as background independent models for dynamical generation of supersymmetric fuzzy spaces, in which quantum corrections are under control.

16 pages

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Cited by in corpus (12)

• Colored Tensor Models - a Review
• Random tensor models in the large N limit: Uncoloring the colored tensor models
• Phase Transition in Dually Weighted Colored Tensor Models
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• Invitation to Random Tensors
• The Double Scaling Limit in Arbitrary Dimensions: A Toy Model
• Canonical tensor models with local time
• Uniqueness of canonical tensor model with local time
• Canonical tensor model through data analysis -- Dimensions, topologies, and geometries --
• Tensor models and 3-ary algebras
• Aspects of quantum gravity
• Fuzzy spaces from tensor models, cyclicity condition, and n-ary algebras