Non-perturbative studies of N=2 conformal quiver gauge theories

Abstract

We study N=2 super-conformal field theories in four dimensions that correspond to mass-deformed linear quivers with n gauge groups and (bi-)fundamental matter. We describe them using Seiberg-Witten curves obtained from an M-theory construction and via the AGT correspondence. We take particular care in obtaining the detailed relation between the parameters appearing in these descriptions and the physical quantities of the quiver gauge theories. This precise map allows us to efficiently reconstruct the non-perturbative prepotential that encodes the effective IR properties of these theories. We give explicit expressions in the cases n=1,2, also in the presence of an Omega-background in the Nekrasov-Shatashvili limit. All our results are successfully checked against those of the direct microscopic evaluation of the prepotential a la Nekrasov using localization methods.

56 pages, 7 figures, PdfLaTeX. v2: a few references added, version to appear on Fortschritte der Physik

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• $T$, $Q$ and periods in $SU(3)$ $\mathcal{N}=2$ SYM
• Modular anomaly equations and S-duality in N=2 conformal SQCD
• VEV of Baxter's Q-operator in N=2 gauge theory and the BPZ differential equation
• A Surprising Relation for the Effective Coupling Constants of N=2 Super Yang-Mills Theories
• Deformed SW curve and the null vector decoupling equation in Toda field theory
• Modular properties of surface operators in N=2 SQCD