高阶形式BRST反常的经典阴影

中文摘要 AI 辅助

我们精确表述了BRST反常可能具有经典相空间阴影的含义。它是在协变相空间上哈密顿对称作用的非等变类。为组织这一表述，我们引入Weil协变相空间双复形，其基本子复形控制等变哈密顿提升。随后我们将这一纯经典类与局部BRST下降进行比较。对于哈密顿可容许的混合转降，鬼数二后代$a^{2}_{d-1}$定义了到荷代数的去鬼化映射，该映射由Cartan代表未能等变所生成。诱导的上同调类独立于Bardeen型下降代表的变化。因此，经典反常是BRST反常的阴影，其精确含义是两者都是同一Weil转降类的实现，同时属于不同理论的对象。作为显式例子，我们分析五维流入转降，并展示经典荷上闭链与BRST后代作为同一Weil转降类的两个实现出现。

英文摘要

We formulate a precise sense in which a BRST anomaly may possess a classical phase space shadow. It is the non-equivariance class of a Hamiltonian symmetry action on covariant phase space. To organize this statement, we introduce the Weil covariant phase space bicomplex, whose basic subcomplex controls equivariant Hamiltonian lifts. We then compare this purely classical class with local BRST descent. For a Hamiltonian admissible mixed transgression, the ghost-number-two descendant $a^{2}_{d-1}$ defines a deghostification map to the charge algebra, which is generated by the failure of the Cartan representative to be equivariant. The induced cohomology class is independent of Bardeen type changes of descent representative. Thus the classical anomaly is a shadow of the BRST anomaly in the precise sense that both are realizations of the same Weil transgression class, while remaining objects of different theories. As an explicit example, we analyze a five dimensional inflow transgression and show that the classical charge cocycle and the BRST descendant arise as two realizations of the same Weil transgression class.

发表机构

• Nanchang University（南昌大学）
• Center for Relativistic Astrophysics and High Energy Physics, Nanchang University（南昌大学相对论天体物理与高能物理中心）
• Jiluan academy, Nangchang University（南昌大学极链学院）
• Department of Physics, Nanchang University（南昌大学物理学院）

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