论文标题
3D扭曲的R-Poisson Sigma模型的BV动作
The BV action of 3D twisted R-Poisson sigma models
论文作者
论文摘要
我们确定了具有Wess-Zumino项的3D拓扑场理论的经典主方程的解决方案，以及其目标空间上扭曲的R-Poisson歧管的基础几何结构。目标空间的分级几何形状与拓扑Sigma模型的AKSZ构造中遇到的通常的QP结构背道而驰，这归因于Wess-Zumino 4形式的障碍物。在这种情况下，由于AKSZ构造的不适当性，我们在任何维度上设置了传统的BV/BRST形式主义，用于扭曲的R-Poisson Sigma模型，该模型具有开放量表代数，并构成了多个阶段，可减少可限制的汉密尔顿系统。理论的一个不寻常的特征是它表现出量规代数的非线性开放性，换句话说，运动方程式出现了。然而，我们在3D中存在4形扭曲的情况下发现了BV动作，即用于特定的4形扭曲（前）Courant Sigma模型。此外，我们为在任何维度中的未透视R-Poisson Sigma模型的脱机Nilpotent BV运算符提供了一套明确的公式。
We determine the solution to the classical master equation for a 3D topological field theory with Wess-Zumino term and an underlying geometrical structure of a twisted R-Poisson manifold on its target space. The graded geometry of the target space departs from the usual QP structure encountered in the AKSZ construction of topological sigma models, the obstruction being attributed to the presence of the Wess-Zumino 4-form. Due to the inapplicability of the AKSZ construction in this case, we set up the traditional BV/BRST formalism for twisted R-Poisson sigma models in any dimension, which feature an open gauge algebra and constitute multiple stages reducible constrained Hamiltonian systems. An unusual feature of the theories is that it exhibits non-linear openness of the gauge algebra, in other words products of the equations of motion appear in it. Nevertheless, we find the BV action in presence of the 4-form twist in 3D, namely for a specific 4-form twisted (pre-)Courant sigma model. Moreover, we provide a complete set of explicit formulas for the off-shell nilpotent BV operator for untwisted R-Poisson sigma models in any dimension.
