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Abstract:
I will discuss a class of four-dimensional integrable quantum field theories which arise from local field theories on twistor space. The main example is the 4d WZW model of Donaldson, Losev, Nekrasov, Moore and Shatashvili, for the group SO(8). Even though these theories are non-renormalizable by power-counting, I will show that they can be constructed at the quantum level, and have many remarkable properties.