Perturbative and Geometric Analysis of the Quartic Kontsevich Model

The analogue of Kontsevich's matrix Airy function, with the cubic potential Tr(Φ³) replaced by a quartic term Tr(Φ⁴) 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 dis...

Ausführliche Beschreibung

Gespeichert in:
Bibliographische Detailangaben
Veröffentlicht in:Symmetry, Integrability and Geometry: Methods and Applications
Datum:2021
Hauptverfasser: Branahl, Johannes, Hock, Alexander, Wulkenhaar, Raimar
Format: Artikel
Sprache:Englisch
Veröffentlicht: Інститут математики НАН України 2021
Online Zugang:https://nasplib.isofts.kiev.ua/handle/123456789/211442
Tags: Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Zitieren:Perturbative and Geometric Analysis of the Quartic Kontsevich Model. Johannes Branahl, Alexander Hock and Raimar Wulkenhaar. SIGMA 17 (2021), 085, 33 pages

Institution

Digital Library of Periodicals of National Academy of Sciences of Ukraine
Beschreibung
Zusammenfassung:The analogue of Kontsevich's matrix Airy function, with the cubic potential Tr(Φ³) replaced by a quartic term Tr(Φ⁴) 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 us to explore critical phenomena in the quartic Kontsevich model.
ISSN:1815-0659