2023-01-24 Seminar Report

On January 20, Nobuo Iida from the Tokyo Institute of Technology gave a talk titled “Math and Physics of Seiberg-Witten theory” at the iTHEMS math seminar. He started by explaining a wide range of reviews in physics such as classical theory, relativity, quantum mechanics, and quantum field theory. Specially, these explanations were prepared for non-physicists and stimulated discussions.
Also, his explanation of these theories contained many instructive examples of such theories which enable us to understand his talk easily.
At the end of the first part, he focused on three kinds of QFTs: free theory, perturbative theory, and more general QFT, and introduced renormalization which gives interactions between high energy theory and low energy theory.
Secondly, he started to explain general motivational questions in geometry on the mathematical side. This part is also prepared for non-mathematician.
After reviewing the history of topology, he introduces Donaldson’s theory and Donaldson’s polynomial invariant, and Witten’s field-theoretic interpretation (topological twist of N=2 SUSY Yang-Mills theory) of the invariant. As the low energy effective theory of N=2 SUSY Yang-Mills theory, a family of gauge theories parametrized by so-called u-plane was introduced.
By analyzing the family and using duality and topological twist, an idea of the Witten conjecture was shared, which relates Donaldson’s polynomial invariant with the Seiberg-Witten invariant on the mathematical side.
His talk was very interesting and stimulated many questions and discussions. I believe it was a very worthwhile time for many participants.

Reported by Masaki Taniguchi

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