Relative formality theorem and quantisation of coisotropic submanifolds
By Alberto S. Cattaneo, Giovanni Felder. 2005
187 citations recorded by the source corpus.
We prove a relative version of Kontsevich's formality theorem. This theorem involves a manifold M and a submanifold C and reduces to Kontsevich's theorem if C=M. It states that the DGLA of multivector fields on an infinitesimal neighbourhood of C is L∞-quasiisomorphic to the DGLA of multidifferential operators acting on sections of the exterior algebra of the conormal bundle. Applications to the deformation quantisation of coisotropic submanifolds are given. The proof uses a duality transformation to reduce the theorem to a version of Kontsevich's theorem for supermanifolds, which we also discuss. In physical language, the result states that there is a duality between the Poisson sigma model on a manifold with a D-brane and the Poisson sigma model on a supermanifold without branes (or, more properly, with a brane which extends over the whole supermanifold).
Subfields: Algebra and Number Theory, Mathematical Physics, Pathology and Forensic Medicine
View Paper: https://www.semanticscholar.org/paper/5295a7dff98d3af81651f98dc2a3951114c2db2a
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Citations in the corpus
- Lectures on Duflo isomorphisms in Lie algebra and complex geometry (2011, methodology): “The proof is strongly based on Kontsevich’s original idea, but actually differs from it (the two approaches are related by a conjectural Koszul type duality recently pointed out in [30], this duality being itself a manifestation of Cattaneo-Felder constructions for the quantization of a Poisson mani”
- Derived coisotropic structures II: stacks and quantization (2017, background): “ the general case of coisotropic structure on a morphism of derived Artin stacks. For example, let L→Xbe a smooth coisotropic submanifold of a Poisson manifold. Then Oh–Park [OP] and Cattaneo–Felder [CF] construct a certain homotopy P1-algebra which as a graded commutative algebra coincides with Γ(L”