Solution of all quartic matrix models
Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar
Research article in digital collection | Preprint | Peer reviewedAbstract
We consider the quartic analogue of the Kontsevich model, which is defined by a measure exp(−NTr(EΦ2+(λ/4)Φ4))dΦ on Hermitean N×N-matrices, where E is any positive matrix and λ a scalar. We prove that the two-point function is a rational function evaluated at roots of another rational function J constructed from the spectrum of E. This rationality is strong support for the conjecture that the quartic analogue of the Kontsevich model is integrable. We also solve the large-N limit to unbounded operators E. The renormalised two-point function is given by an integral formula involving a regularisation of J.
Details about the publication
Name of the repository: arXiv
Article number: 1906.04600
Status: submitted / under review
Release year: 2019 (11/06/2019)
Language in which the publication is written: English
Link to the full text: https://arxiv.org/abs/1906.04600
Keywords: matrix models; solvable non-linear integral equations; integrability; complex curves
Authors from the University of Münster
| Hock, Alexander | Professur für Reine Mathematik (Prof. Wulkenhaar) |
| Wulkenhaar, Raimar | Professur für Reine Mathematik (Prof. Wulkenhaar) |