Formal loops IV: Chiral differential operators

Abstract

We relate the gerbe of sheaves of chiral differential operators (CDO) on a algebraic variety X, studied by Gorbounov, Malikov and Schechtman, to the determinantal gerbe of the formal loop space LX introduced in our earlier paper. The liens of the two gerbes are related by a version of the symplectic action homomorphism. The determinantal gerbe of LX has a factorization structure in the spirit of Beilinson and Drinfeld. In our identification, sheaves of CDO correspond to factorizing objects of this factorization gerbe.

References in corpus (1)

• Formal loops III: Factorizing functions and the Radon transform

Cited by in corpus (8)

• Universal factorization spaces and algebras
• Higher dimensional formal loop spaces
• Equivariant localization in factorization homology and applications in mathematical physics I: Foundations
• Formal loops III: Factorizing functions and the Radon transform
• Equivariant localization in factorization homology and applications in mathematical physics II: Gauge theory applications
• Half-integrable modules over algebras of twisted chiral differential operators
• Chiral vector bundles
• Mixed anomalies of chiral algebras compactified to smooth quasi-projective surfaces