Formal Global AKSZ Gauge Observables and Generalized Wilson Surfaces

Covariance of the classical Brink-Schwarz superparticle

We show that the classical Brink-Schwarz superparticle is a generalized AKSZ field theory. We work in the Batalin-Vilkovisky formalism: the main technical tool is the vanishing of Batalin--Vilkovisky cohomology below degree -1.

The Poisson sigma model on closed surfaces

Using methods of formal geometry, the Poisson sigma model on a closed surface is studied in perturbation theory. The effective action, as a function on vacua, is shown to have no quantum corrections if the surface is a torus or if the Poisson structure is regular and unimodular (e.g., symplectic). In the case of a Kahler structure or of a trivial Poisson structure, the partition function on the torus is shown to be the Euler characteristic of the target; some evidence is given for this to happen more generally. The methods of formal geometry introduced in this paper might be applicable to othe…

Formal Global Perturbative Quantization of the Rozansky-Witten Model in the BV-BFV Formalism

We describe a globalization construction for the Rozansky-Witten model in the BV-BFV formalism for a source manifold with and without boundary in the classical and quantum case. After having introduced the necessary background, we define an AKSZ sigma model, which, upon globalization through notions of formal geometry extended appropriately to our case, is shown to reduce to the Rozansky-Witten model. The relations with other relevant constructions in the literature are discussed. Moreover, we split the model as a $BF$-like theory and we construct a perturbative quantization of the model in th…

Mixed symmetry Wilson-loop interactions in the worldline formalism

Using the worldline formalism of the Dirac field with a non-Abelian gauge symmetry we show how to describe the matter field transforming in an arbitrary representation of the gauge group. Colour degrees of freedom are carried on the worldline by auxiliary fields, responsible for providing path ordering and the Wilson-loop coupling. The Hilbert space of these fields is reducible but we make use of recent work in order to project onto a single, arbitrary, irreducible representation. By functionally quantising the resulting theory we show that this procedure correctly generates the Wilson-loop in…

Batalin-Vilkovisky形式中的高维BF理论：BV作用和广义Wilson环

Higher-dimensional BF theories in the Batalin-Vilkovisky formalism: The BV action and generalized Wilson loops

本文详细分析了n维流形上BF理论的Batalin-Vilkovisky量子化过程，并描述了一种合适的超性能化方法来处理主方程和观测量的搜索。特别是，广义威尔逊循环BF理论与额外的多项式B-相互作用进行了讨论，在任何维度。文中还对数学QA/0003073中的定理给出了明确的证明。

$L_\infty$-Algebra Models and Higher Chern-Simons Theories

We continue our study of zero-dimensional field theories in which the fields take values in a strong homotopy Lie algebra. In a first part, we review in detail how higher Chern-Simons theories arise in the AKSZ-formalism. These theories form a universal starting point for the construction of $L_\infty$-algebra models. We then show how to describe superconformal field theories and how to perform dimensional reductions in this context. In a second part, we demonstrate that Nambu-Poisson and multisymplectic manifolds are closely related via their Heisenberg algebras. As a byproduct of our discuss…

李代数体态射、Poisson Sigma模型和离壳闭规范对称性

Lie algebroid morphisms, Poisson Sigma Models, and off-shell closed gauge symmetries

三维的陈-西蒙斯规范理论和二维的泊松-西格玛模型（PSM）是同一理论的例子，如果它们的场方程被解释为李代数胚的态射，它们的对称性（在壳上）被解释为这种态射的同伦。我们指出，（离壳）规范对称性的PSM在文献中不是全球良好定义的非平行泊松流形，并提出了一个协变定义，他们作为左作用的一些有限维李代数体。我们的方法可以避免BV-和AKSZ-形式主义的无限维超几何中出现的并发症。这个预印本是一系列论文的起点，旨在介绍李代数胚的杨-米尔斯型规范理论，其中包括和推广标准YM理论，PSM和gerbes。

BV-BFV形式体系中的4流形拓扑、Donaldson-Witten理论、Floer同调与高阶规范理论方法

4-Manifold Topology, Donaldson-Witten Theory, Floer Homology and Higher Gauge Theory Methods in the BV-BFV Formalism

本文在BV-BFV形式体系中重构带边4流形的Donaldson-Witten理论，证明其满足修正量子主方程，并联系Nekrasov配分函数、高阶规范理论与枚举几何。

几何（2+1）引力和Chern-Simons公式：嫁接、Dehn扭曲、威尔逊圈观测量和宇宙学常数

Geometrical (2+1)-gravity and the Chern-Simons formulation: Grafting, Dehn twists, Wilson loop observables and the cosmological constant

本文将（2+1）维引力的几何描述和Chern-Simons描述联系起来，其中$S_g$是亏格$g>1$的有向双曲面，对于Lorentz签名和一般宇宙学常数，以及具有负宇宙学常数的欧几里德情形.我们展示了如何参数化的陈-西蒙斯形式主义的相空间的变量是从几何描述和几何结构的（2+1）-时空通过嫁接沿封闭的，简单的测地线产生的相空间上的变换。我们证明，这些变换是通过泊松括号中的两个典型的威尔逊圈观测量之一产生的测地线，而另一个行为作为无穷小德恩扭曲的哈密顿量。对于具有洛伦兹签名的时空，我们讨论了宇宙学常数作为形变参数在几何和陈-西蒙斯理论表述中的作用。特别地，我们证明了Chern-Simons规范群的李代数可以与交换环上的（2+1）维Lorentz代数相一致，其特征在于形式参数$Θ_Λ$的平方是减去宇宙学常数。在这个框架中，产生嫁接和Dehn扭曲的威尔逊圈可观察量被获得为环中值可观察的威尔逊圈的实分量和$Θ_Λ$分量，并且嫁接变换可以被视为具有参数$Θ_Λ$的无限小Dehn扭曲。

弦拓扑的拓扑域论解释

Topological Field Theory Interpretation of String Topology

Chas和Sullivan [math.GT/9911159]引入的弦括号从Batalin-Vilkovisky或BRST形式化中的拓扑域论的观点重新解释。也就是说，拓扑作用泛函规范场（推广陈-西蒙斯和BF理论）被认为是与广义威尔逊回路。后者产生一个（泊松或Gerstenhaber）代数的泛函与价值观的$S^1$ -等变上同调的闭路空间的流形上的理论定义。证明了在$GL_n$具有标准表示的情况下，两个广义Wilson环对两个圈的（Poisson或BV）括号与广义Wilson环对这两个圈的弦括号的（Poisson或BV）括号相同.概括到其他群体的简要说明。