1212.4972 (Jean-Emile Bourgine)

Large N techniques for Nekrasov partition functions and AGT conjecture    [PDF]

Jean-Emile Bourgine

The AGT conjecture relates \mathcal{N}=2 4d SUSY gauge theories to 2d CFTs. Matrix model techniques can be used to investigate both sides of this relation. The large N limit refers here to the size of Young tableaux in the expression of the gauge theory partition function. It corresponds to vanishing of Omega-background equivariant deformation parameters, and should not be confused with the t'Hooft expansion at large number of colors. In the first part of the paper, a saddle point approach is employed to study the Nekrasov-Shatshvili limit of the gauge theory, leading to define beta-deformed, or quantized, Seiberg-Witten curve and differential form. In a second part, this formalism is compared to the large N limit of the Dijkgraaf-Vafa beta-ensemble. A transformation law relating the wave functions appearing at both sides of the conjecture is proposed. It implies a transformation of the Seiberg-Witten 1-form in agreement with the definition proposed earlier. As a side result, a remarkable property of the \mathcal{N}=2 theory emerged: the instanton contribution to the partition function can be determined from the pertubative term analysis.

View original: http://arxiv.org/abs/1212.4972