Deformation of Batalin-Vilkovisky Structures

Batalin-Vilkovisky 形式中的同伦

Homotopies in Batalin-Vilkovisky Formalism

本文回顾几何Batalin-Vilkovisky形式中量子主作用的同伦概念，构造来自重整化群流和非无穷小规范固定变化的同伦新例子，并利用这些同伦给出的场重定义构造具有同构有效作用的量子主作用跨。

Poisson cohomology, Koszul duality, and Batalin-Vilkovisky algebras

We study the noncommutative Poincaré duality between the Poisson homology and cohomology of unimodular Poisson algebras, and show that Kontsevich's deformation quantization as well as Koszul duality preserve the corresponding Poincaré duality. As a corollary, the Batalin-Vilkovisky algebra structures that naturally arise in these cases are all isomorphic.

Solving the noncommutative Batalin-Vilkovisky equation

I show that a summation over ribbon graphs with legs gives the construction of the solutions to the noncommutative Batalin-Vilkovisky equation, including the equivariant version. This generalizes the known construction of A-infinity algebra via summation over ribbon trees. These solutions give naturally the supersymmetric matrix action functionals, which are the gl(N)-equivariantly closed differential forms on the matrix spaces, which were introduced in one of my previous papers "Noncommmutative Batalin-Vilkovisky geometry and Matrix integrals" (arXiv:0912.5484, electronic CNRS preprint hal-00…

Introduction to Graded Geometry, Batalin-Vilkovisky Formalism and their Applications

These notes are intended to provide a self-contained introduction to the basic ideas of finite dimensional Batalin-Vilkovisky (BV) formalism and its applications. A brief exposition of super- and graded geometries is also given. The BV-formalism is introduced through an odd Fourier transform and the algebraic aspects of integration theory are stressed. As a main application we consider the perturbation theory for certain finite dimensional integrals within BV-formalism. As an illustration we present a proof of the isomorphism between the graph complex and the Chevalley-Eilenberg complex of for…

Modular operads and Batalin-Vilkovisky geometry

This is a copy of the article published in IMRN (2007). I describe the noncommutative Batalin-Vilkovisky geometry associated naturally with arbitrary modular operad. The classical limit of this geometry is the noncommutative symplectic geometry of the corresponding tree-level cyclic operad. I show, in particular, that the algebras over the Feynman transform of a twisted modular operad P are in one-to-one correspondence with solutions to quantum master equation of Batalin-Vilkovisky geometry on the affine P-manifolds. As an application I give a construction of characteristic classes with values…

Batalin--Vilkovisky 量子化与超对称扭曲

Batalin--Vilkovisky quantization and supersymmetric twists

本文证明了以 Kähler 为目标的超对称力学拓扑扭曲存在 Batalin--Vilkovisky 量子化，并基于特定反常层上同调提出拓扑扭曲后 Hilbert 空间的一般构造，给出了多个实例验证。