|DATE||September 30 (Thu), 2021|
|TITLE||An E8 surprise|
Jacobi forms are everywhere in physics whenever a torus and a non-abelian gauge/flavor symmetry is involved. In 1992 Wirthmuller proved that for any root system of type A,B,C,D,G,F and E6,E7, the ring of weak Jacobi forms invariant under Weyl group is a polynomial algebra. However, it was recently proved by Haowu Wang that for E8, the ring is not a polynomial algebra. I will discuss how to describe E8 Weyl invariant Jacobi forms properly and how to use them in physics, such as the elliptic genera of E-strings.