报告题目：Modular factorization of superconformal index

报告人： 雷扬 副教授（苏州大学高等研究院）

报告时间：2023年03月23日（周四）下午15:00-16:00

报告地点：在线报告（腾讯会议ID：825 9224 6730）

报告摘要：

Superconformal indices of four-dimensional N=1 gauge theories factorize into holomorphic blocks. We interpret this as a modular property resulting from the combined action of an SL(3,Z) and SL(2,Z)⋉Z2 transformation. The former corresponds to a gluing transformation and the latter to an overall large diffeomorphism, both associated with a Heegaard splitting of the underlying geometry. The extension to more general transformations leads us to argue that a given index can be factorized in terms of a family of holomorphic blocks parametrized by modular (congruence sub)groups. We find precise agreement between this proposal and new modular properties of the elliptic Γ function. This allows us to establish the ``modular factorization'' of superconformal lens indices of general N=1 gauge theories. Based on this result, we systematically prove that a normalized part of superconformal lens indices defines a non-trivial first cohomology class associated with SL(3,Z). Finally, we use this framework to propose a formula for the general lens space index.

参考文献：

- Kevin Goldstein, Vishnu Jejjala, Yang Lei, Sam van Leuven, Wei Li, Residues, modularity, and the Cardy limit of the 4d N = 4 superconformal index, JHEP 04 (2021) 216, [arXiv: 2011.06605 [hep-th]].

- Vishnu Jejjala, Yang Lei, Sam van Leuven, Wei Li, SL(3, ℤ) Modularity and New Cardy limits of the N = 4 superconformal index, JHEP 11 (2021) 047, [arXiv: 2104.07030 [hep-th]].

- Vishnu Jejjala, Yang Lei, Sam van Leuven, Wei Li, Modular factorization of superconformal indices, arXiv: 2210.17551 [hep-th].

报告人简介：

雷扬于2011年毕业于北京大学元培学院物理专业和数学双学位，于2011-2016年在Durham大学获得博士学位。之后分别在中国科学院理论物理研究所，南非金山大学，丹麦Niels Bohr研究所和中国科学院大学担任过博士后研究职务。现任苏州大学物理科学与技术学院以及高等研究院副教授。