Two tales of one N=4 chiral algebra

          @misc{ pirsa_PIRSA:25110071,
            doi = {10.48660/25110071},
            url = {https://pirsa.org/25110071},
            author = {Li, Wei},
            keywords = {Mathematical physics},
            language = {en},
            title = {Two tales of one N=4 chiral algebra},
            publisher = {Perimeter Institute},
            year = {2025},
            month = {nov},
            note = {PIRSA:25110071 see, \url{https://pirsa.org}}
          }
          

Abstract

The N=4 chiral algebra is a vertex operator algebra generated by the Schur subsector of the 4D N=4 SYM theory, and it can be obtained by applying the holomorphic-topological twist to the theory in the presence of the Omega-background. For the first part of the talk, I will discuss how the N=4 chiral algebra arises from the worldsheet perspective, using a conjectured worldsheet CFT dual of the 4D N=4 U(N) SYM at the free point. Then for the second part of the talk, I will view the N=4 chiral algebra as an abstract VOA and try to determine its structure using only the associativity of the OPE. We find that the algebra is uniquely characterized by the central charge (which can take an arbitrary value), without any additional free parameter. Furthermore, the truncation pattern of the OPE coefficients suggests that the algebra cannot arise from the symmetric orbifold.