Discussion 4

Ring objects in the equivariant derived Satake category and 3d N=4 QFT

The mathematical definition of Coulomb branches of 3d N=4 gauge theories gives ring objects in the equivariant derived Satake category. We have another fundamental example of a ring object, namely the regular sheaf. It corresponds to the 3d N=4 QFT T[G], studied by Gaiotto-Witten. We also have operations on ring objects, corresponding to products, restrictions, Coulomb/Higgs gauging in the `category' of 3d N=4 QFT's. Thus we conjecture that arbitrary 3d N=4 QFT with G-symmetry gives rise a ring object in the derived Satake for G.

Borcherds-Kac-Moody Algebras, Moonshine VOAs, and String Theory

In this talk we will review our physical proposal, with D. Persson and R. Volpato, to understand the genus zero property of monstrous moonshine. The latter was proven by Borcherds in 1992 by brute-force computation but has since resisted a conceptual understanding. We embed the Monster VOA of Frenkel-Lepowsky-Meurman into a heterotic string compactification and use physical arguments, i.e. T-dualities and decompactification limits, to understand the genus zero property.

The Master Chiral Algebra

Discussion 2