12:00 pm Monday, April 3, 2023
Junior GST: Geometric Engineering for 4d N=2 Supersymmetric Quantum Field Theory by
Wang Yao (UT Austin) in PMA 9.166
Geometric engineering is a method to construct quantum field theories via the reduction of certain higher dimensional theories on certain geometric spaces. The properties of the resulting QFT is determined by the geometry of the space. In my talk, I will focus on the geometric engineering of 4d N=2 SUSY field theory. The geometric construction of 4d N=2 SUSY field theory is to reduce the type IIA string theory on a toric Calabi-Yau Threefold to decouple the gravity. In this case, the process of geometric engineering can be done via the local mirror symmetry of toric Calabi-Yau Threefolds. To be more specific, the mirror manifold of the toric Calabi-Yau Threefold, after suitable dimensional reduction, is precisely the Seiberg-Witten curve of the resulting 4d N=2 SUSY. Geometric engineering provides us with another way to study QFT, which is quite different from the traditional Lagrangian method. In fact, we could get the information of some QFTs without even knowing the Lagrangians. My talk will be divided into three parts. Firstly, I will briefly introduce 4d N=2 SUSY, Coulomb Branch and the Seiberg-Witten theory of the Coulomb Branch. Secondly, I will briefly introduce toric varieties and the local mirror symmetry of toric CY3. Finally, I will introduce the process of the geometric engineering for 4d N=2 SUSY. I will mainly focus on SU(2) gauge theory and may make some remarks on more complicated gauge groups. Due to the time limit, I will not include too many details in my talk and will refer the audiences to some references. Submitted by
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