The problem of constructing gauge-invariant actions for conformal higher-spin fields in curved backgrounds is known to be notoriously difficult. In this paper we present gauge-invariant models for conformal maximal depth fields with spin s = 5/2 and s = 3 in four-dimensional Bach-flat backgrounds. We find that certain lower-spin fields must be introduced to ensure gauge invariance when s > 2, which is analogous to a conjecture made earlier in the literature for conformal higher-spin fields of minimal depth.

中文翻译：

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弯曲背景中的广义共形高自旋场

众所周知，在弯曲背景中为共形高自旋场构造规范不变动作的问题是出了名的困难。在本文中，我们提出了四维巴赫平坦背景中自旋 s = 5/2 和 s = 3 的共形最大深度场的规范不变模型。我们发现，当 s > 2 时，必须引入某些低自旋场以确保规范不变性，这类似于文献中早期对最小深度的共形高自旋场所做的猜想。