|Speaker:||Junya Yagi (Rutgers Univ.)|
|Title:||Chiral Algebras of (0,2) Models: Beyond Perturbation Theory|
|Date:||Mon, Nov 30, 2009, 16:30 - 18:00|
|Place:||Room 002, Mathematical Sciences Building, Komaba Campus|
The chiral algebras of two-dimensional sigma models with (0,2) supersymmetry are infinite-dimensional generalizations of the chiral rings of (2,2) models. Perturbatively, they enjoy rich mathematical structures described by sheaves of chiral differential operators. Nonperturbatively, however, they vanish completely for certain (0,2) models with no left-moving fermions. In this talk, I will explain how this vanishing phenomenon takes places. The vanishing of the chiral algebra of a (0, 2) model implies that supersymmetry is
spontaneously broken in the model, which in turn suggests that no harmonic spinors exist on the loop space of the target space. In
particular, the elliptic genus of the model vanishes, thereby providing a physics proof of a special case of the Hoelhn-Stolz conjecture.