Details

Autor(en) / Beteiligte

• Klemm, Albrecht
• Mariño, Marcos
• Rauch, Marco

Titel

Direct integration and non-perturbative effects in matrix models

Ist Teil von

• The journal of high energy physics, 2010-10, Vol.2010 (10), Article 4

Ort / Verlag

Berlin/Heidelberg: Springer-Verlag

Erscheinungsjahr

2010

Link zum Volltext

Quelle

Springer Journals

Beschreibungen/Notizen

• We show how direct integration can be used to solve the closed amplitudes of multicut matrix models with polynomial potentials. In the case of the cubic matrix model, we give explicit expressions for the ring of nonholomorphic 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 onedimensional submanifold of the moduli space in which the spectral curve becomes the Seiberg-Witten curve and the ring reduces to the nonholomorphic 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 nonperturbative effects due to instantons. Finally, we argue that a full understanding of the large genus asymptotics in the multicut case requires a new class of nonperturbative sectors in the matrix model.