Correspondence between Feynman diagrams and operators in quantum field theory that emerges from tensor model

Abstract

A novel functorial relationship in perturbative quantum field theory is pointed out that associates Feynman diagrams (FD) having no external line in one theory ${\mathbf{Th}}_1$ with singlet operators in another one ${\mathbf{Th}}_2$ having an additional $U(\mathcal{N})$ symmetry and is illustrated by the case where ${\mathbf{Th}}_1$ and ${\mathbf{Th}}_2$ are respectively the rank $r-1$ and the rank $r$ complex tensor model. The values of FD in ${\mathbf{Th}}_1$ agree with the large $\mathcal{N}$ limit of the Gaussian average of those operators in ${\mathbf{Th}}_2$. The recursive shift in rank by this FD functor converts numbers into vectors, then into matrices, and then into rank $3$ tensors $\dots$ This FD functor can straightforwardly act on the $d$ dimensional tensorial quantum field theory 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.

arXiv comment5 pages

References in corpus (14)

• Matrix Models, Topological Strings, and Supersymmetric Gauge Theories
• Chiral Rings and Anomalies in Supersymmetric Gauge Theory
• On Geometry and Matrix Models
• Matrix models vs. Seiberg-Witten/Whitham theories
• Counting Tensor Model Observables and Branched Covers of the 2-Sphere
• On the complete perturbative solution of one-matrix models
• The Dijkgraaf-Vafa prepotential in the context of general Seiberg-Witten theory
• Correlators in tensor models from character calculus
• Ward identities and combinatorics of rainbow tensor models
• Rainbow tensor model with enhanced symmetry and extreme melonic dominance
• Cut and join operator ring in Aristotelian tensor model
• Catalog of dessins d'enfants with \le 4 edges
• Toric CFTs, Permutation Triples, and Belyi Pairs
• Generalized cut operation associated with higher order variation in tensor models

Cited by in corpus (2)

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