M5-branes, toric diagrams and gauge theory duality
Journal article, 2012

In this article we explore the duality between the low energy effective theory of five-dimensional N = 1 SU(N)(M-1) and SU(M)(N-1) linear quiver gauge theories compactified on S-1. The theories we study are the five-dimensional uplifts of four-dimensional superconformal linear quivers. We study this duality by comparing the Seiberg-Witten curves and the Nekrasov partition functions of the two dual theories. The Seiberg-Witten curves are obtained by minimizing the worldvolume of an M5-brane with nontrivial geometry. Nekrasov partition functions are computed using topological string theory. The result of our study is a map between the gauge theory parameters, i.e., Coulomb moduli, masses and UV coupling constants, of the two dual theories. Apart from the obvious physical interest, this duality also leads to compelling mathematical identities. Through the AGTW conjecture these five-dimentional gauge theories are related to q-deformed Liouville and Toda SCFTs in two-dimensions. The duality we study implies the relations between Liouville and Toda correlation functions through the map we derive.


topological string amplitudes


n=2 supersymmetric

liouville field-theory

conformal blocks




matrix models

integrable systems

Supersymmetry and Duality


Topological Strings

yang-mills theory


Ling Bao

Chalmers, Applied Physics, Subatomic Physics

E. Pomoni

Humboldt University of Berlin

M. Taki

Kyoto University

F. Yagi

Istituto Nazionale Di Fisica Nucleare, Frascati

Journal of High Energy Physics

1126-6708 (ISSN) 1029-8479 (eISSN)


Subject Categories

Physical Sciences



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