Chiral Algebras of (0,2) Models

Details Chiral Algebras of (0,2) Models Chiral Algebras of (0,2) Models

2010-01-04

arxiv.org/abs/1001.0118v3

Physics

High Energy Physics

High Energy Physics - Theory

38 pages. This is a revised version of chapters 1-4 of the author's thesis. The thesis is available electronically from Rutger

Scientific paper

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.

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