My master's thesis investigates the Zhu algebra of vertex operator algebras (VOAs) arising from the 4D N=2 SCFT/VOA duality. Based on the foundational work of Beem and collaborators (arXiv:1312.5344), this duality establishes a correspondence between a 4D N=2 superconformal field theory (SCFT) and a VOA. A central conjecture in this framework suggests that the associated variety of the VOA is isomorphic to the Higgs branch of the corresponding 4D N=2 SCFT.
Additionally, Bonetti, Meneghelli, and Rastelli (arXiv:1810.03612) showed that a complex reflection group can be used to construct an N=2 superconformal vertex algebra (SCVA). In the specific case where the reflection group is the Weyl group of a simple Lie algebra—such as sl_n—this leads to an N=2 SCVA derived from the 4D N=4 supersymmetric Yang-Mills theory with gauge group SL_n.
The primary objective of my research is to compute the (twisted) Zhu algebra of this N=2 SCVA. Where the twisted Zhu algebra provides a systematic framework for understanding the (twisted) representation theory of the SCVA.
Here is link to the pdf.