Ricardo Schiappa, Niclas Wyllard
Published 2009-11-30, updated 2010-01-24Version 3
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.
Comments: 43 pages; v2: minor typos corrected, reference added. v3: Added clarifying discussions in sections 4.1 and 5.1; typos corrected
$\widehat{\mathfrak{sl}}(n)_N$ WZW conformal blocks from $SU(N)$ instanton partition functions on ${\mathbb {C}}^2/{\mathbb {Z}}_n$
N=2 superconformal blocks and instanton partition functions
(p,q)-webs of DIM representations, 5d N=1 instanton partition functions and qq-characters
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