Generalized cut operation associated with higher order variation in tensor models

Abstract

The cut and join operations play important roles in tensor models in general. We introduce a generalization of the cut operation associated with the higher order variations and demonstrate how they generate operators in the Aristotelian tensor model. We point out that, by successive choices of appropriate variations, the cut operation generalized this way can generate those operators which do not appear in the ring of the join operation, providing a tool to enumerate the operators by a level by level analysis recursively. We present a set of rules that control the emergence of such operators.

13 pages, 1 figure; v2: minor corrections made, a reference added

References in corpus (8)

• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• The complete $1/N$ expansion of a SYK--like tensor model
• All point correlation functions in SYK
• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models