An A_r threesome: Matrix models, 2d CFTs and 4d N=2 gauge theories

Abstract

We explore the connections between three classes of theories: A_r quiver matrix models, d=2 conformal A_r Toda field theories and d=4 N=2 supersymmetric conformal A_r quiver gauge theories. In particular, we analyse the quiver matrix models recently introduced by Dijkgraaf and Vafa and make detailed comparisons with the corresponding quantities in the Toda field theories and the N=2 quiver gauge theories. We also make a speculative proposal for how the matrix models should be modified in order for them to reproduce the instanton partition functions in quiver gauge theories in five dimensions.

43 pages; v2: minor typos corrected, reference added. v3: Added clarifying discussions in sections 4.1 and 5.1; typos corrected

References in corpus (9)

• The Refined Topological Vertex
• On AGT relation in the case of U(3)
• On non-conformal limit of the AGT relations
• Correlation functions in conformal Toda field theory I
• The Power of Nekrasov Functions
• Zamolodchikov asymptotic formula and instanton expansion in N=2 SUSY N_f=2N_c QCD
• Proving AGT relations in the large-c limit
• Seiberg-Witten theory and matrix models
• Matrix models for 2* theories

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