Perturbative and Geometric Analysis of the Quartic Kontsevich Model
| Autor: | Johannes Branahl, Raimar Wulkenhaar, Alexander Hock |
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| Rok vydání: | 2021 |
| Předmět: |
High Energy Physics - Theory
81T18 81T16 14H81 32A20 Toy model Series (mathematics) FOS: Physical sciences Mathematical Physics (math-ph) symbols.namesake High Energy Physics - Theory (hep-th) Airy function Quartic function Ribbon symbols Feynman diagram Geometry and Topology Quantum field theory Mathematical Physics Analysis Mathematics Mathematical physics Meromorphic function |
| Zdroj: | Symmetry, Integrability and Geometry: Methods and Applications. |
| ISSN: | 1815-0659 |
| Popis: | The analogue of Kontsevich's matrix Airy function, with the cubic potential $\operatorname{Tr}\big(\Phi^3\big)$ replaced by a quartic term $\operatorname{Tr}\big(\Phi^4\big)$ with the same covariance, provides a toy model for quantum field theory in which all correlation functions can be computed exactly and explicitly. In this paper we show that distinguished polynomials of correlation functions, themselves given by quickly growing series of Feynman ribbon graphs, sum up to much simpler and highly structured expressions. These expressions are deeply connected with meromorphic forms conjectured to obey blobbed topological recursion. Moreover, we show how the exact solutions permit to explore critical phenomena in the quartic Kontsevich model. Comment: 33 pages, 13 figures. v2: distinction between our model and GKM, exact formula for genus zero closed graphs, example higher-order ramification: correct limit. Small corrections. v3: some material added to sec 5.1+5.3. v4: published version |
| Databáze: | OpenAIRE |
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