论文标题
Bach-Flat背景中的新的本地（超级）共形量规模型
New locally (super)conformal gauge models in Bach-flat backgrounds
论文作者
论文摘要
对于每个在四个维度上的保形量规场$ h_ {α（n）\dotα（m）} $，并带有$ n \ geq m> 0 $，已知在任意固定的背景中存在量规不变的动作。但是，如果Weyl张量是非呈现的，则量规不变性在以下情况下具有纯粹的共形场：（i）$ n = m = 1 $（麦克斯韦的磁场）在任意重力背景上； （ii）$ n = m+1 = 2 $（共形gravitino）和$ n = m = 2 $（共形栅栏）在bach-flat背景上。人们认为，在其他情况下，必须引入某些下旋转字段以确保在Bach-Flat背景中的规格不变性，尽管尚未构建封闭形式模型（除了Spin $ s = 5/2 $和$ S = 3 $的保形最大深度场除外）。在本文中，我们得出了描述保形量规场$ H_ {α（3）\dotα} $耦合到自动划分两种形式的量规数模型。类似于其他保形的高旋转理论，它可以嵌入非壳超符号量规动作中。为此，我们介绍了一个新的家庭，由$ \ Mathcal {n} = 1 $ super-Congrongumal量规多重；由无约束的预势率$υ_{α（n）} $，带有$ n> 0 $，并提出了对正态flatswords的相应仪表式的动作。我们证明，可以将$ n = 2 $模型在组件级别包含$ h_ {α（3）\dotα} $，可以将提供给提供$υ_{α（2）} $的bach-flat背景，并耦合到手化旋转纺纱$ $ω__α$。我们还提出了（超级）在任何弯曲空间中（超级）高衍生的非规范行动和新的超符合操作员的家庭。最后，通过基于超对称性的考虑，我们认为相结合的Spin-3场应始终伴随着保形的Spin-2场，以确保在Bach-Flat背景中的规格不变性。
For every conformal gauge field $h_{α(n)\dot α(m)}$ in four dimensions, with $n\geq m >0$, a gauge-invariant action is known to exist in arbitrary conformally flat backgrounds. If the Weyl tensor is non-vanishing, however, gauge invariance holds for a pure conformal field in the following cases: (i) $n=m=1$ (Maxwell's field) on arbitrary gravitational backgrounds; and (ii) $n=m+1 =2 $ (conformal gravitino) and $n=m=2$ (conformal graviton) on Bach-flat backgrounds. It is believed that in other cases certain lower-spin fields must be introduced to ensure gauge invariance in Bach-flat backgrounds, although no closed-form model has yet been constructed (except for conformal maximal depth fields with spin $s=5/2$ and $s=3$). In this paper we derive such a gauge-invariant model describing the dynamics of a conformal gauge field $h_{α(3)\dotα}$ coupled to a self-dual two-form. Similar to other conformal higher-spin theories, it can be embedded in an off-shell superconformal gauge-invariant action. To this end, we introduce a new family of $\mathcal{N}=1$ superconformal gauge multiplets described by unconstrained prepotentials $Υ_{α(n)}$, with $n>0$, and propose the corresponding gauge-invariant actions on conformally-flat backgrounds. We demonstrate that the $n=2$ model, which contains $h_{α(3)\dotα}$ at the component level, can be lifted to a Bach-flat background provided $Υ_{α(2)}$ is coupled to a chiral spinor $Ω_α$. We also propose families of (super)conformal higher-derivative non-gauge actions and new superconformal operators in any curved space. Finally, through considerations based on supersymmetry, we argue that the conformal spin-3 field should always be accompanied by a conformal spin-2 field in order to ensure gauge invariance in a Bach-flat background.
