Abstract
We propose, following the AGT correspondence, how the {mathcal{W}}_{N,n}^{mathrm{para}} (n-th parafermion {mathcal{W}}_N ) minimal model characters are obtained from the U(N ) instanton counting on ℂ2/ℤn with Ω-deformation by imposing specific conditions which remove the minimal model null states.
Highlights
We propose, following the AGT correspondence, how the WNpa,nra (n-th parafermion WN ) minimal model characters are obtained from the U(N ) instanton counting on C2/Zn with Ω-deformation by imposing specific conditions which remove the minimal model null states
The AGT correspondence [1] with various generalizations makes the connection between 4D supersymmetric gauge theory with Ω-deformation [2] and 2D conformal field theory (CFT) with a generic central charge
In this paper we will focus on the correspondence between a 4D N = 2 U(N ) supersymmetric gauge theory on C2/Zn and a 2D CFT with the symmetry algebra
Summary
The AGT correspondence [1] with various generalizations makes the connection between 4D supersymmetric gauge theory with Ω-deformation [2] and 2D conformal field theory (CFT) with a generic central charge. In this paper we will focus on the correspondence between a 4D N = 2 U(N ) supersymmetric gauge theory on C2/Zn and a 2D CFT with the symmetry algebra. For the gauge theory with an adjoint hypermultiplet, the AGT-corresponding CFT lives on a torus T 2. In the case of 1 + 2 = 0 (corresponding to p → ∞), the U(N ) instanton partition function on C2/Zn for the massless adjoint hypermultiplet yields the partition function of an N = 4 twisted Yang-Mills theory enumerating torus fixed points on the moduli space of instantons, which is labelled by N -tuples of n-coloured Young diagrams The twisted partition function is well-known to give a character of the 2D CFT [17,18,19], where a string theory interpretation is given in [20]
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