Chiral de Rham complex on Riemannian manifolds and special holonomy

Abstract

Interpreting the chiral de Rham complex (CDR) as a formal Hamiltonian quantization of the supersymmetric non-linear sigma model, we suggest a setup for the study of CDR on manifolds with special holonomy. We show how to systematically construct global sections of CDR from differential forms, and investigate the algebra of the sections corresponding to the covariantly constant forms associated with the special holonomy. As a concrete example, we construct two commuting copies of the Odake algebra (an extension of the N=2 superconformal algebra) on the space of global sections of CDR of a Calabi-Yau threefold and conjecture similar results for G_2 manifolds. We also discuss quasi-classical limits of these algebras.

49 pages, title changed, major rewrite with no changes in the main theorems, published version

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Cited by in corpus (10)

• Lambda: A Mathematica-package for operator product expansions in vertex algebras
• $\mathcal{G}$-structure symmetries and anomalies in $(1,0)$ non-linear $\sigma$-models
• Recent advances and open questions on the susy structure of the chiral de Rham Complex
• The global sections of chiral de Rham complexes on compact Ricci-flat Kähler manifolds II
• Vector bundles induced from jet schemes
• Sheaves of N=2 supersymmetric vertex algebras on Poisson manifolds
• $\mathcal{S}\mathcal{W}$-algebras and strings with torsion
• The global sections of chiral de Rham complexes on compact Ricci-flat Kähler manifolds
• A commutant realization of Odake's algebra
• ${\mathrm{G}}_2$ holonomy manifolds are superconformal