Matrix models for β-ensembles from Nekrasov partition functions
- Creators
- Sułkowski, Piotr
Abstract
We relate Nekrasov partition functions, with arbitrary values of ϵ_1, ϵ_2 parameters, to matrix models for β-ensembles. We find matrix models encoding the instanton part of Nekrasov partition functions, whose measure, to the leading order in ϵ_2 expansion, is given by the Vandermonde determinant to the power β = −ϵ_1/ϵ_2. An additional, trigonometric deformation of the measure arises in five-dimensional theories. Matrix model potentials, to the leading order in ϵ_2 expansion, are the same as in the β = 1 case considered in 0810.4944 [hep-th]. We point out that potentials for massive hypermultiplets include multi-log, Penner-like terms. Inclusion of Chern-Simons terms in five-dimensional theories leads to multi-matrix models. The role of these matrix models in the context of the AGT conjecture is discussed.
Additional Information
© SISSA 2010. Received: 3 February 2010. Accepted: 2 April 2010. Published online: 16 April 2010. I am grateful to Robbert Dijkgraaf, Hiroaki Kanno, Albrecht Klemm, Nikita Nekrasov, Niclas Wyllard, and especially Bertrand Eynard for discussions, correspondence, and remarks on the manuscript. I thank George Gasper, Mourad Ismail, Yaming Yu and Ruiming Zhang for correspondence on various asymptotics. I also thank IPhT-CEA Saclay for hospitality. This research was supported by the DOE grant DE-FG03-92ER40701FG-02, the Foundation for Polish Science, and the European Commission under the Marie-Curie International Outgoing Fellowship Programme. The contents of this publication reflect only the views of the author and not the views of the funding agencies.Additional details
- Eprint ID
- 18543
- Resolver ID
- CaltechAUTHORS:20100603-085257715
- DE-FG03-92ER40701FG-02
- Department of Energy (DOE)
- Foundation for Polish Science
- European Commission
- Created
-
2010-06-18Created from EPrint's datestamp field
- Updated
-
2021-11-08Created from EPrint's last_modified field