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 (26)

• Critical behavior of colored tensor models in the large N limit
• Uncolored Random Tensors, Melon Diagrams, and the SYK Models
• A Generalization of Sachdev-Ye-Kitaev
• The Bulk Dual of SYK: Cubic Couplings
• The complete $1/N$ expansion of a SYK--like tensor model
• All point correlation functions in SYK
• $O(N)$ Random Tensor Models
• Diagrammatics of a colored SYK model and of an SYK-like tensor model, leading and next-to-leading orders
• A generalization of the Virasoro algebra to arbitrary dimensions
• Revisiting random tensor models at large N via the Schwinger-Dyson equations
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• The Schwinger Dyson equations and the algebra of constraints of random tensor models at all orders
• On the complete perturbative solution of one-matrix models
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Gauge Invariants, Correlators and Holography in Bosonic and Fermionic Tensor Models
• Quenched equals annealed at leading order in the colored SYK model
• Cut-and-Join operator representation for Kontsevich-Witten tau-function
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Tensor Models, Kronecker coefficients and Permutation Centralizer Algebras
• Sum rules for characters from character-preservation property of matrix models
• Cut and join operator ring in Aristotelian tensor model
• Tensor models from the viewpoint of matrix models: the case of loop models on random surfaces
• Open intersection numbers, Kontsevich-Penner model and cut-and-join operators
• From Kronecker to tableau pseudo-characters in tensor models
• On $W$-representations of $\beta$- and $q,t$-deformed matrix models

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• Backgrounds from Tensor Models: A Proposal
• Review on the Operator/Feynman diagram/Dessins d'enfant Correspondence in Tensor Model