PIRSA:20020019

Noncommutative Zhu algebra and quantum field theory in four and three dimensions

Dedushenko, M. (2020). Noncommutative Zhu algebra and quantum field theory in four and three dimensions. Perimeter Institute. https://pirsa.org/20020019

Dedushenko, Mykola. Noncommutative Zhu algebra and quantum field theory in four and three dimensions. Perimeter Institute, Feb. 25, 2020, https://pirsa.org/20020019 

          @misc{ pirsa_PIRSA:20020019,
            doi = {10.48660/20020019},
            url = {https://pirsa.org/20020019},
            author = {Dedushenko, Mykola},
            keywords = {Quantum Fields and Strings},
            language = {en},
            title = {Noncommutative Zhu algebra and quantum field theory in four and three dimensions},
            publisher = {Perimeter Institute},
            year = {2020},
            month = {feb},
            note = {PIRSA:20020019 see, \url{https://pirsa.org}}
          }

Mykola Dedushenko

Stony Brook University

Talk number
PIRSA:20020019
Collection
Talk Type
Subject
Abstract

For any vertex operator algebra V, Y. Zhu constructed an associative algebra Zhu(V) that captures its representation theory (more generally, given a finite order automorphism g of V, there exists an algebra Zhu_g(V) that captures g-twisted representation theory of V). 

To a 4d N=2 superconformal theory T, one assigns a vertex algebra V[T] by the construction of Beem et al. We explain one role of Zhu algebra in this context. Namely, we show that a certain quotient of the Zhu algebra describes what happens to the Schur sector of the theory T under the dimensional reduction on S^1. This connects the VOA construction in 4d N=2 SCFT to the topological quantum mechanics construction in 3d N=4 SCFT, with the latter being given by the aforementioned quotient of the Zhu algebra. In the process, we will discuss how to reformulate the VOA construction on an S^3 x S^1 geometry.