Bimodules and Branes in Deformation Quantization

نویسنده

  • CARLO A. ROSSI
چکیده

We prove a version of Kontsevich’s formality theorem for two subspaces (branes) of a vector space X. The result implies in particular that the Kontsevich deformation quantizations of S(X∗) and ∧(X) associated with a quadratic Poisson structure are Koszul dual. This answers an open question in Shoikhet’s recent paper on Koszul duality in deformation quantization.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

Coisotropic Submanifolds in Poisson Geometry and Branes in the Poisson Sigma Model

General boundary conditions (“branes”) for the Poisson sigma model are studied. They turn out to be labeled by coisotropic submanifolds of the given Poisson manifold. The role played by these boundary conditions both at the classical and at the perturbative quantum level is discussed. It turns out to be related at the classical level to the category of Poisson manifolds with dual pairs as morph...

متن کامل

Bimodule deformations, Picard groups and contravariant connections

We study deformations of invertible bimodules and the behavior of Picard groups under deformation quantization. While K0-groups are known to be stable under formal deformations of algebras, Picard groups may change drastically. We identify the semiclassical limit of bimodule deformations as contravariant connections and study the associated deformation quantization problem. Our main focus is on...

متن کامل

Deformation quantization as the origin of D-brane non-Abelian degrees of freedom

I construct a map from the Grothendieck group of coherent sheaves to Khomology. This results in explicit realizations of K-homology cycles associated with D-brane configurations. Non-Abelian degrees of freedom arise in this framework from the deformation quantization of N -tuple cycles. The large N limit of the gauge theory on D-branes wrapped on a subvariety V of some variety X is geometricall...

متن کامل

Deformation Quantization and Reduction

This note is an overview of the Poisson sigma model (PSM) and its applications in deformation quantization. Reduction of coisotropic and prePoisson submanifolds, their appearance as branes of the PSM, quantization in terms of L∞and A∞-algebras, and bimodule structures are recalled. As an application, an “almost” functorial quantization of Poisson maps is presented if no anomalies occur. This le...

متن کامل

5 Poisson - Dirac branes in Poisson - Sigma models by Iván Calvo and Fernando Falceto

We analyse the general boundary conditions (branes) consistent with the Poisson-sigma model and study the structure of the phase space of the model defined on the strip with these boundary conditions. Finally, we discuss the perturbative quantization of the model on the disc with a PoissonDirac brane and relate it to Kontsevich’s formula for the deformation quantization of the Dirac bracket ind...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2009