Blobbed topological recursion of the quartic Kontsevich model I: Loop equations and conjectures
Johannes Branahl, Alexander Hock, Raimar Wulkenhaar
备注：
53 pages, 13 figures. v2: proofs in appendix E considerably simplified, typos corrected. v3: added reference arXiv:2103.13271, where we have proved the main conjecture for $g=0$. v4: rearrangements to improve readability, graphical interpretation of loop equations added, analogies to the 2-matrix model emphasised
发表信息：
Communications in Mathematical Physics 393, 1529-1582 (2022)
We provide strong evidence for the conjecture that the analogue of Kontsevich's matrix Airy function, with the cubic potential $\mathrm{Tr}(Φ^3)$ replaced by a quartic term $\mathrm{Tr}(Φ^4)$, obeys the blobbed topological recursion of Borot and Shadrin. We identify in the quartic Kontsevich model three families of correlation functions for which we establish interwoven loop equations. One family consists of symmetric meromorphic differential forms $ω_{g,n}$ labelled by genus and number of marked points of a complex curve. We reduce the solution of all loop equations to a straightforward but lengthy evaluation of residues. In all evaluated cases, the $ω_{g,n}$ consist of a part with poles at ramification points which satisfies the universal formula of topological recursion, and of a part holomorphic at ramification points for which we provide an explicit residue formula.
Blobbed topological recursion and KP integrability
Center for Geometry and Physics, Institute for Basic Science (IBS)（基础科学研究院几何物理中心）；Department of Mathematics, University of Haifa（海法大学数学系）；Faculty of Mathematics, HSE University（高等经济大学数学系）；HSE–Skoltech International Laboratory of Representation Theory and Mathematical Physics, Skoltech（俄罗斯高等经济大学-斯科尔科沃学院表示论与数学物理国际实验室，斯科尔科沃学院）；NRC “Kurchatov Institute” – ITEP（库尔恰托夫国家研究中心-理论物理研究所）；Igor Krichever Center for Advanced Studies, Skoltech（斯科尔科沃学院伊戈尔·克里切弗高级研究中心）；Korteweg-de Vries Institute for Mathematics, University of Amsterdam（阿姆斯特丹大学科特韦格-德弗里斯数学研究所）
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