https://doi.org/10.1140/epjc/s10052-020-8013-8
Letter
Correspondence between Feynman diagrams and operators in quantum field theory that emerges from tensor model
1
A.I. Alikhanov Institute for Theoretical and Experimental Physics of NRC “Kurchatov Institute”, B. Cheremushkinskaya, 25, Moscow, 117259, Russia
2
National Research University “Higher School of Economics”, Myasnitskaya Ul., 20, Moscow, 101000, Russia
3
Institute for Information Transmission Problems of RAS (Kharkevich Institute), Bolshoy Karetny per. 19, build.1, Moscow, 127051, Russia
4
Nambu Yoichiro Institute of Theoretical and Experimental Physics (NITEP), Osaka, Japan
5
Department of Mathematics and Physics, Graduate School of Science, Osaka City University, Osaka, Japan
6
Osaka City University Advanced Mathematical Institute (OCAMI), 3-3-138, Sugimoto, Sumiyoshi-ku, Osaka, 558-8585, Japan
7
I.E.Tamm Theory Department, Lebedev Physics Institute, Leninsky prospect, 53, Moscow, 119991, Russia
8
Kavli Institute for Theoretical Physics, Konh Hall, UC Santa Barbara, Santa Barbara, CA, 93106-4030, USA
9
Moscow Institute of Physics and Technology, Dolgoprudny, 141701, Russia
* e-mail: mironov@lpi.ru
** e-mail: mironov@itep.ru
Received:
21
February
2020
Accepted:
3
May
2020
Published online:
26
May
2020
A novel functorial relationship in perturbative quantum field theory is pointed out that associates Feynman diagrams (FD) having no external line in one theory 
with singlet operators in another one 
having an additional 
symmetry and is illustrated by the case where and are respectively the rank 
and the rank r complex tensor model. The values of FD in agree with the large 
limit of the Gaussian average of those operators in . The recursive shift in rank by this FD functor converts numbers into vectors, then into matrices, then into rank 3 tensors and so on. This FD functor can straightforwardly act on the d dimensional tensorial quantum field theory (QFT) counterparts as well. In the case of rank 2-rank 3 correspondence, it can be combined with the geometrical pictures of the dual of the original FD, namely, equilateral triangulations (Grothendieck’s dessins d’enfant) to form a triality which may be regarded as a bulk-boundary correspondence.
© The Author(s), 2020
