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Ellipticity and modularity in integrable systems, and N=1*

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Elliptic integrable systems arise as low-energy effective superpotentials of supersymmetric gauge theories. Their extrema sometimes form vector valued modular forms of congruent subgroups of the modular group. We will find confirmations of this fact, as well as exceptions. We find for instance a point of monodromy at rational Klein invariant. We construct the duality diagrams of the extrema of low rank integrable systems, and will discuss further intriguing number theoretic properties of the extrema. We apply all the knowledge we obtain to the physics of N=1* gauge theories with B,C and D type gauge algebra.

This talk is part of the Quantum Fields and Strings Seminars series.

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