Chiral Algebras of (0,2) Models

Abstract

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 Kähler manifolds, this suggests that there are no harmonic spinors on their loop spaces and gives a physical proof of the Höhn-Stolz conjecture.

28 pages. This is a revised version of chapters 1-4 of the author's thesis. The thesis is available electronically from Rutgers University Library; Adv. Theor. Math. Phys. 16 (2012) 1

References in corpus (5)

• Phases of $N=2$ Theories In Two Dimensions
• Mirror Manifolds And Topological Field Theory
• Chiral de Rham complex and the half-twisted sigma-model
• Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory - II
• Chiral Algebras of (0,2) Sigma Models: Beyond Perturbation Theory

Cited by in corpus (12)

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• Chiral algebras from Ω-deformation
• A 2d (0,2) appetizer
• N=(0, 2) Deformation of (2, 2) Sigma Models: Geometric Structure, Holomorphic Anomaly and Exact Beta Functions
• B-branes and supersymmetric quivers in 2d
• On the six-dimensional origin of the AGT correspondence
• On Isometry Anomalies in Minimal N=(0,1) and N=(0,2) Sigma Models
• A domain wall in twisted M-theory
• On Grassmannian Heterotic Sigma Model
• Making supersymmetric connected N =(0,2) Sigma Models
• More on Two-Dimensional $O(N)$ Models with $\mathcal{N}=(0,1)$ Supersymmetry
• Vanishing Chiral Algebras and Höhn-Stolz Conjecture