No subtopics of Algebraic Geometry
- Vanishing Chiral Algebras and H\"ohn-Stolz Conjecture
- Renormalization Group and the Ricci flow
- Conformal superspace sigma-models
- On the Kodaira dimension of maximal orders
Chiral Algebras of (0,2) Models
We explore two-dimensional sigma models with (0,2) supersymmetry through their chiral algebras. Perturbatively, the chiral algebras of (0,2) models have a rich infinite-dimensional structure described by the cohomology of a sheaf of chiral differential operators. Nonperturbatively, instantons can deform this structure drastically. We show that under some conditions they even annihilate the whole algebra, thereby triggering the spontaneous breaking of supersymmetry. For a certain class of K\"ahler manifolds, this suggests that there are no harmonic spinors on their loop spaces and gives a physical proof of the H\"ohn-Stolz conjecture.