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arXiv · 1610.00526

Exact solution of matricial $Φ^3_2$ quantum field theory

Harald Grosse·Akifumi Sako·Raimar Wulkenhaar
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Abstract

We apply a recently developed method to exactly solve the $Φ^3$ 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 $Φ^3$ 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.

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Harald Grosse, Akifumi Sako, Raimar Wulkenhaar. 2017-06-02. Exact solution of matricial $Φ^3_2$ quantum field theory. https://doi.org/10.1016/j.nuclphysb.2017.10.010

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