论文标题
Quantum Chern-Simons在圆柱体上的理论：BV-BFV分区功能
Quantum Chern-Simons theories on cylinders: BV-BFV partition functions
论文作者
论文摘要
我们计算Chern-Simons类型的分区函数，用于圆柱形空间$ i \ timesσ$，在BV-BFV形式主义（Batalin-vilkovisky的形式上的改进）中，每间隔$ i $ $ i $ i $ i $ i \ i \ i \ timesσ$，$ \ \ dim = 4l+2 $，适合于边界和切割和切割的薄膜）。 $ \dimσ= 0 $被视为玩具示例。我们表明，可以识别出（对于某些选择残留场）的某些选择 - 与同伴论文中计算出的汉密尔顿 - 雅各比（Hamilton -Jacobi）动作的BV -BFV有效作用的“物理部分”（限制为零字段）[arxiv：2012.13270]，没有任何量子校正。这种汉密尔顿 - 雅各比（Hamilton-Jacobi）动作是$σ$的共形场理论的动作功能。对于$ \dimσ= 2 $，这意味着CS-WZW通信的版本。对于$ \ dimσ= 6 $，使用圆柱体的一端的特定极化，Chern-Simons分区函数与Kodaira-Spencer Gravity有关（又称BCOV理论）；这提供了Gerasimov和Shatashvili对半经典结果的BV-BFV量子透视。
We compute partition functions of Chern-Simons type theories for cylindrical spacetimes $I \times Σ$, with $I$ an interval and $\dim Σ= 4l+2$, in the BV-BFV formalism (a refinement of the Batalin-Vilkovisky formalism adapted to manifolds with boundary and cutting-gluing). The case $\dim Σ= 0$ is considered as a toy example. We show that one can identify - for certain choices of residual fields - the "physical part" (restriction to degree zero fields) of the BV-BFV effective action with the Hamilton-Jacobi action computed in the companion paper [arXiv:2012.13270], without any quantum corrections. This Hamilton-Jacobi action is the action functional of a conformal field theory on $Σ$. For $\dim Σ= 2$, this implies a version of the CS-WZW correspondence. For $\dim Σ= 6$, using a particular polarization on one end of the cylinder, the Chern-Simons partition function is related to Kodaira-Spencer gravity (a.k.a. BCOV theory); this provides a BV-BFV quantum perspective on the semiclassical result by Gerasimov and Shatashvili.
