# Generalized cut operation associated with higher order variation in tensor models

## TL;DR

This paper introduces a generalized cut operation linked to higher order variations in tensor models, enabling the generation and enumeration of operators beyond those accessible by join operations, thus advancing the analysis of tensor model operators.

## Contribution

It proposes a new generalized cut operation associated with higher order variations, allowing recursive enumeration of tensor model operators beyond traditional methods.

## Key findings

- The generalized cut operation can generate operators not produced by join operations.
- A recursive level-by-level analysis method for tensor operators is developed.
- Rules controlling the emergence of new operators are established.

## 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.