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In this talk, I will consider the orbi-instanton theories and their dimensional reductions on the 2-torus. In particular, I shall focus on the cases of type D. Unlike the A-type ones, it turns out that not all of the theories are described by the class S theories (with three untwisted regular punctures on the sphere). I will mention how the class S theories (and the 3d mirror quivers) can be read off from the tensor branch descriptions of the 6d theories. As the orbi-instanton theories are labelled by the discrete homomorphisms from the dicyclic groups to E_8, the discussions would also shed light on the classifications of these homomorphisms, such as some partial labels of the homomorphisms, and certain one-to-two correspondences due to the theta angles (which is similar to but different from the one-to-two correspondences for the very even D-type nilpotent orbits). Moreover, I will discuss some Higgsings that are “hidden” from the punctures, but are still manifest from the 6d. This is based on the work with Noppadol Mekareeya, Gabi Zafrir, and Hao Y. Zhang.
Bio: Jiakang Bao is a postdoc at the University of Tokyo. He completed his PhD at City, University of London under the supervision of Yang-Hui He. His research mainly focuses on supersymmetric gauge theories and their connections to different aspects in mathematics.
Prof. Yinan Wang