Abstract
It is shown that the deformed Seiberg-Witten curve equation after Fourier transform is mapped into a differential equation for the AGT dual 2d CFT cnformal block containing an extra completely degenerate field. We carefully match parameters in two sides of duality thus providing not only a simple independent prove of the AGT correspondence in Nekrasov-Shatashvili limit, but also an extension of AGT to the case when a secondary field is included in the CFT conformal block. Implications of our results in the study of monodromy problems for a large class of n’th order Fuchsian differential equations are discussed.
Highlights
Deformed Seiberg-Witten curve for Ar quiverIn the case of Ar quiver theory with fundamental and bi-fundamental matter hypermultiplets and unitary U(n) gauge groups (see figure 1a), there is an n-tuple of Young diagrams associated to each of the r gauge groups (indicated by circles in figure 1a)
With 2d CFT called the AGT correspondence [10,11,12]
The algebraic equations defining SW curve get replaced by difference equations
Summary
In the case of Ar quiver theory with fundamental and bi-fundamental matter hypermultiplets and unitary U(n) gauge groups (see figure 1a), there is an n-tuple of Young diagrams associated to each of the r gauge groups (indicated by circles in figure 1a) It has been shown in [18] for the case of a single gauge group and later generalized further in [19,20,21] that among all fixed points in moduli space of instantons there is a unique one giving a non-vanishing. 2.1 Exponents 2.1.1 Points zr+2 = 0 and z0 = ∞ First let’s look after a solution of the form ψ(z) = zs(1 + O(z)) Inserting this in (2.18) we see that when z → 0 the term with α = r +1 of (2.18) is the most singular one.
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