标题： 对常曲率时空上的规范场的环境空间变分法 显示英文标题

标题： Ambient-space variational calculus for gauge fields on constant-curvature spacetimes

摘要： 我们提出了一种系统生成过程，从平坦环境空间$\mathbb{R}^{d,2}$中无质量场的BRST拉格朗日描述出发，构建在$AdS_{d+1}$上质量、无质量和部分质量的完全对称张量场的自由拉格朗日量。 一个新颖之处在于，拉格朗日量由$\mathbb{R}^{d,2}$上的一个$d+1$形式描述，其在$AdS_{d+1}$上的拉回给出了定义在反德西特时空上的真实拉格朗日量。 我们的推导使用了源自一阶量子化BRST方法的三元组形式，其中作用原理由BRST算子和一阶量子化系统的内积决定。 通过这种方式，我们以明显地$so(2,d)$-协变的方式构建了一个统一的作用原理，适用于上述三种类型的场。 特别是，我们的推导证明了早期为AdS上质量场和无质量场提出的某些作用形式的正确性。 我们还以各自切丛和变分双复形的形式给出了环境拉格朗日量的一般框架。 特别是，我们引入了一个合适的环境空间欧拉-拉格朗日微分，允许以环境方式推导运动方程，即不需要显式推导相应的时空拉格朗日量。 显示英文摘要

摘要： We propose a systematic generating procedure to construct free Lagrangians for massive, massless and partially massless, totally-symmetric tensor fields on $AdS_{d+1}$ starting from the BRST Lagrangian description of massless fields in the flat ambient space $\mathbb{R}^{d,2}$. A novelty is that the Lagrangian is described by a $d+1$ form on $\mathbb{R}^{d,2}$ whose pullback to $AdS_{d+1}$ gives the genuine Lagrangian defined on anti de Sitter spacetime. Our derivation uses the triplet formulation originating from the first-quantized BRST approach, where the action principle is determined by the BRST operator and the inner product of a first-quantised system. In this way we build, in a manifestly $so(2,d)$-covariant manner, a unifying action principle for the three types of fields mentioned above. In particular, our derivation justifies the form of some actions proposed earlier for massive and massless fields on AdS. We also give a general setup for ambient Lagrangians in terms of the respective jet-bundles and variational bi-complexes. In particular we introduce a suitable ambient-space Euler-Lagrange differential which allows to derive the equation of motion ambiently, i.e. without the need to explicitly derive the respective spacetime Lagrangian.