Kazunobu Maruyoshi

Penner type matrix model and Seiberg-Witten theory

We discuss the Penner type matrix model recently proposed by Dijkgraaf and Vafa for a possible explanation of the relation between four-dimensional gauge theory and Liouville theory by making use of the connection of the matrix model to two-dimensional CFT. We first consider the relation of gauge couplings defined in UV and IR regimes of Nf = 4,

Seiberg-Witten theory, matrix model and AGT relation

\mathcal{N}

Seiberg-Witten curve via generalized matrix model

= 2 supersymmetric gauge theory being related as qUV = ϑ2(qIR)4/ϑ3(qIR)4. We then use this relation to discuss the action of modular transformation on the matrix model and determine its spectral curve.We also discuss the decoupling of massive flavors from the Nf = 4 matrix model and derive matrix models describing asymptotically free

N=2 quiver gauge model and partial supersymmetry breaking

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U(N) GAUGED

= 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of