2010/02/22 by Albrecht Klemm, Marcos Mariño, Marcos Marino +1 · 34 citations
Mathematics · Physics and Astronomy · #Algebraic structures and combinatorial models #Anomaly (physics) #Black Holes and Theoretical Physics #Genus #Holomorphic function #Matrix (chemical analysis) #Modular design #Moduli space #Parametrization (atmospheric modeling) #Polynomial #Quantum Chromodynamics and Particle Interactions #Ring (chemistry) #hep-th
paper · pdf · doi:10.1007/jhep10(2010)004
published in Journal of High Energy Physics 2010(10) (Springer Nature) · 51 pages, 8 figures
arxiv created 2010/02/22 · openalex publication_date 2010/10/01 · arxiv updated 2010/12/01 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
We show how direct integration can be used to solve the closed amplitudes of multi-cut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of non-holomorphic modular objects that are needed to express all closed matrix model amplitudes. This allows us to integrate the holomorphic anomaly equation up to holomorphic modular terms that we fix by the gap condition up to genus four. There is an one-dimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg--Witten curve and the ring reduces to the non-holomorphic modular ring of the group Γ(2). On that submanifold, the gap conditions completely fix the holomorphic ambiguity and the model can be solved explicitly to very high genus. We use these results to make precision tests of the connection between the large order behavior of the 1/N expansion and non-perturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multi-cut case requires a new class of non-perturbative sectors in the matrix model.