Katherine Maxwell (MPIM Bonn)
Tuesday, November 9, 2021 - 14:00
HU Berlin, Institut für Physik, IRIS-Haus
Zum Großen Windkanal 2, 12489 Berlin-Adlershof, Raum 1'021, https://hu-berlin.zoom.us/j/61686623112
Hybrid seminar: Algebra, Geometry and Physics (HU Berlin/MPIM Bonn)
Gaetan Borot (HU Berlin), Yuri Manin (MPIM)
In 1986, Manin conjectured that representations of the Neveu-Schwarz (NS) algebra must be related to the moduli space of SUSY curves. We present a new way to explain this relationship which utilizes the super Sato Grassmannian. This method is a super generalization of the classical story of Kontsevich; Arbarello, De Concini, Kac, and Procesi; and Kawamoto, Namikawa, Tsuchiya, and Yamada. We find that the Lie superalgebra of global superconformal vector fields on an affine SUSY curve is perfect, and that the NS algebra acts on the line bundle of the super Mumford isomorphism with zero central charge. We discuss why this new approach may have interesting applications for integrating over the moduli space of SUSY curves.
submitted by Gaetan Borot (gaetan.borot@hu-berlin.de)