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Solutions of Four Dimensional Field Theories Via M Theory


I'm going to talk about the classic Witten paper "Solutions of Four-Dimensional Field Theories Via M Theory" [1].

Seiberg-Witten theory gives us the exact low-energy effective action for 4 dimensional N=2 theories on the Coulomb branch. In [1] Witten shows how one can obtain the SW curve for a large class of N=2 theories which are the world-volume gauge theories living on D4 branes which are part of a type IIA brane setup also involving NS5 branes. This is done by lifting to M theory and observing that the equation for the SW curve has a geometric interpretation. Also given is a geometric interpretation of the beta function for the gauge coupling constants.

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