论文标题
边界手性代数和全体形态曲折
Boundary Chiral Algebras and Holomorphic Twists
论文作者
论文摘要
我们研究了边界存在的3d $ {\ cal n} = 2 $量规理论的全态扭曲，以及批量和边界本地操作员的代数结构。在全体形态扭曲中，散装和边界本地操作员形成手性代数（\ emph {a.k.a。}顶点操作员代数）。批量代数是可交换的，具有移动的泊松支架和“更高”的应力张量。虽然边界代数是批量的模块，但可能不交换，也可能没有应力张量。我们明确构建了自由理论和兰道吉堡模型的批量和边界代数。我们通过物质和/或Chern-Simons耦合构建边界代数为仪表理论构建，将批量代数的完整描述留在未来的工作中。我们简要地讨论了较高的afinity结构的存在。
We study the holomorphic twist of 3d ${\cal N}=2$ gauge theories in the presence of boundaries, and the algebraic structure of bulk and boundary local operators. In the holomorphic twist, both bulk and boundary local operators form chiral algebras (\emph{a.k.a.} vertex operator algebras). The bulk algebra is commutative, endowed with a shifted Poisson bracket and a "higher" stress tensor; while the boundary algebra is a module for the bulk, may not be commutative, and may or may not have a stress tensor. We explicitly construct bulk and boundary algebras for free theories and Landau-Ginzburg models. We construct boundary algebras for gauge theories with matter and/or Chern-Simons couplings, leaving a full description of bulk algebras to future work. We briefly discuss the presence of higher A-infinity like structures.
