Exact solution of matricial \(\Phi^3_2\) quantum field theory

We apply a recently developed method to exactly solve the \(\Phi^3\) matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and S...

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Bibliographic Details
Published inarXiv.org
Main Authors Grosse, Harald, Sako, Akifumi, Wulkenhaar, Raimar
Format Paper
LanguageEnglish
Published Ithaca Cornell University Library, arXiv.org 02.06.2017
Subjects
Covariance
Deformation
Field theory
Graphs
Integral equations
Mathematical models
Quantum field theory
Quantum theory
Two dimensional models
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Summary:We apply a recently developed method to exactly solve the \(\Phi^3\) matrix model with covariance of a two-dimensional theory, also known as regularised Kontsevich model. Its correlation functions collectively describe graphs on a multi-punctured 2-sphere. We show how Ward-Takahashi identities and Schwinger-Dyson equations lead in a special large-\(\mathcal{N}\) limit to integral equations that we solve exactly for all correlation functions. Remarkably, these functions are analytic in the \(\Phi^3\) coupling constant, although bounds on individual graphs justify only Borel summability. The solved model arises from noncommutative field theory in a special limit of strong deformation parameter. The limit defines ordinary 2D Schwinger functions which, however, do not satisfy reflection positivity.
ISSN:2331-8422
DOI:10.48550/arxiv.1610.00526