Penner type matrix model and Seiberg-Witten theory
By Tohru Eguchi, K. Maruyoshi. 2009
165 citations recorded by the source corpus.
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, $$ \mathcal{N} $$ = 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 $$ \mathcal{N} $$ = 2 gauge theories. We find that the Penner type matrix theory reproduces correctly the standard results of $$ \mathcal{N} $$ = 2 supersymmetric gauge theories.
Subfields: Nuclear and High Energy Physics, Statistical and Nonlinear Physics
View Paper: https://www.semanticscholar.org/paper/8cb57106f691c37a2a27c1bf157bcd571244aec7
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In Nuclear and High Energy Physics
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Citations in the corpus
- A& B model approaches to surface operators and Toda thoeries (2010, result): “the topological recursion to compute amptudes 9 for the SU(2) theory with Nf = 4 and compare them to the results in Liouville theory of section 3. The Seiberg-Witten differential is given by (see e.g. [45]): λSW = p P 4(z)dz z(z−1)(z−ζ) , (4.20) with P 4(z) = m2 0 z4 + z3S 1 + z 2S 2 + zS 3 + S 4 = Y”
- Five-Dimensional AGT Relation and the Deformed β-Ensemble (2010, background): “Some explanations have been addressed from β-ensemble (generalized matrix model) [2][3] in [4]–[7].”
- Wild quiver gauge theories (2011, background): “n the specific CFT at hand and having a geometric counterpart of the state building recipe (4.10) would be interesting. Also the role of these states in the matrix model approach to AGT correspondence [76, 77, 78] should be clarified. Our construction of the irregular conformal blocks is shown to be s”