| Description |
Nekrasov used a $U(1)^2$ subgroup of the SO(4) Lorentz symmetry on $R^4$ to define a $U(1)^2$-equivariant version of the topological partition function, or, equivalently, the partition function of the $N= 2$ supersymmetric gauge theory in the Omega-deformed background. The integral over the moduli space of instantons localizes at the fixed point set of a group which acts on the moduli space by Lorentz rotations of the spacetime and gauge transformations at infinity. Pestun gave a new matrix integral which, with all instanton corrections included, is well defined in the $N = 2$, the $N = 2*$ and the $N = 4$ cases, and gives the exact partition function of these theories on S4. The expectation value of a supersymmetric circular Wilson operator on S4 in an arbitrary representation is equal to the expectation value of the operator $Tr_R[exp(2\pi ira)]$ in this matrix model. In the first talk, I will explain the Nekrasov partition function and will talk about Pestun's localization method in the second talk.
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