Generalized cut operation associated with higher order variation in tensor models

Itoyama, H. (Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka City University, Japan) (Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Japan) (Osaka City University Advanced Mathematical Institute (OCAMI), 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan) ; Yoshioka, R. (Osaka City University Advanced Mathematical Institute (OCAMI), 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan)

26 June 2019

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.


Published in: Nuclear Physics B 945 (2019) DOI: 10.1016/j.nuclphysb.2019.114681
License: CC-BY-3.0



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