4D N = 1规范超执行层次的所有Chern-Simons不变量
All Chern-Simons Invariants of 4D, N = 1 Gauged Superform Hierarchies
摘要：
本文给出了四维超空间中超对称引力/（非）阿贝尔$p$ -形式族的几何描述，并给出了超空间中具有$N = 1$超Poincare不变性的超对称引力/（非）阿贝尔$p$-形式族.这些层次结构产生了类似陈-西蒙斯的不变量，如5D、$N = 1$引力光子和11维3-形式的不变量，但也有类似格林-施瓦茨/BF型耦合的推广。以前的建设的基础上prepotential超场重新解释的$p$ -形式在超空间，从而阐明了潜在的几何。这大大简化了超空间场强、比安奇恒等式和陈-西蒙斯不变量的计算。使用这个，我们证明了递归公式的有效性的条件定义这些行动的任何这样的张量层次。在二次和三次阶上求解，我们恢复了BF型和三次Chern-Simons作用的已知结果。作为一个应用，我们计算四次不变$\sim A dA dA dA + \ldots$相关，例如，七维超引力紧化。
英文摘要：
We give a geometric description of supersymmetric gravity/(non-)abelian $p$-form hierarchies in superspaces with 4D, $N = 1$ super-Poincare invariance. These hierarchies give rise to Chern-Simons-like invariants, such as those of the 5D, $N = 1$ graviphoton and the eleven-dimensional 3-form but also generalizations such as Green-Schwarz-like/BF-type couplings. Previous constructions based on prepotential superfields are reinterpreted in terms of $p$-forms in superspace thereby elucidating the underlying geometry. This vastly simplifies the calculations of superspace field-strengths, Bianchi identities, and Chern-Simons invariants. Using this, we prove the validity of a recursive formula for the conditions defining these actions for any such tensor hierarchy. Solving it at quadratic and cubic orders, we recover the known results for the BF-type and cubic Chern-Simons actions. As an application, we compute the quartic invariant $\sim A dA dA dA + \ldots$ relevant, for example, to seven-dimensional supergravity compactifications.
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