Solution of all quartic matrix models

Grosse, Harald; Hock, Alexander; Wulkenhaar, Raimar

Zusammenfassung

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.