PIRSA:22060079

Generalised Langlands, VOAs, and (generalised) tau-functions

Teschner, J. (2022). Generalised Langlands, VOAs, and (generalised) tau-functions. Perimeter Institute. https://pirsa.org/22060079

Teschner, Joerg. Generalised Langlands, VOAs, and (generalised) tau-functions. Perimeter Institute, Jun. 27, 2022, https://pirsa.org/22060079 

          @misc{ pirsa_PIRSA:22060079,
            doi = {10.48660/22060079},
            url = {https://pirsa.org/22060079},
            author = {Teschner, Joerg},
            keywords = {Mathematical physics},
            language = {en},
            title = {Generalised Langlands, VOAs, and (generalised) tau-functions},
            publisher = {Perimeter Institute},
            year = {2022},
            month = {jun},
            note = {PIRSA:22060079 see, \url{https://pirsa.org}}
          }

Joerg Teschner

Deutsches Elektronen-Synchrotron DESY

Talk number
PIRSA:22060079
Collection
Talk Type
Subject
Abstract
In the first part of my talk I'll briefly review some aspects of the relations between N=4, d=4 SYM and vertex operator algebras (VOAs) discussed in recent work of Gaiotto and collaborators. The resulting picture predicts conjectural generalisations of the geometric Langlands correspondence. We will focus on a class of examples figuring prominently in recent work of Creutzig-Dimofte-Garner-Geer, labelled by parameters n (rank) and k. For the case k=1,n=2 we will point out that the conformal blocks of the relevant VOA, twisted by local systems, represent sections of natural holomorphic line bundles over the moduli spaces of local systems closely related to the isomonodromic tau functions. Observing the crucial role of (quantised) cluster algebras in the definition of the holomorphic line bundles suggests natural generalisations of this story to higher values of the parameters k and n.