In U-duality-manifest formulations, supergravity fields are packaged into covariant objects such as the generalized metric and $p$-form fields $\mathcal{A}_p^{I_p}$. While a parameterization of the generalized metric in terms of supergravity fields is known for U-duality groups $E_n$ with $n\leq 8$, a parameterization of $\mathcal{A}_p^{I_p}$ has not been fully determined. In this paper, we propose a systematic method to determine the parameterization of $\mathcal{A}_p^{I_p}$, which necessarily involves mixed-symmetry potentials. We also show how to systematically obtain the T- and S-duality transformation rules of the mixed-symmetry potentials entering the multiplet. As the simplest non-trivial application, we find the parameterization and the duality rules associated with the dual graviton. Additionally, we show that the 1-form field $\mathcal{A}_1^{I_1}$ can be regarded as the generalized graviphoton in the exceptional spacetime.

中文翻译：

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奇异膜和混合对称势 II：对偶规则和特殊的 p 型规范场

在 U-duality-manifest 公式中，超重力场被打包成协变对象，例如广义度量和 $p$-form 字段 $\mathcal{A}_p^{I_p}$。虽然 U 对偶群 $E_n$ 与 $n\leq 8$ 的超重力场方面的广义度量的参数化是已知的，但 $\mathcal{A}_p^{I_p}$ 的参数化尚未完全确定. 在本文中，我们提出了一种系统方法来确定 $\mathcal{A}_p^{I_p}$ 的参数化，这必然涉及混合对称势。我们还展示了如何系统地获得进入多重态的混合对称势的 T 和 S 对偶变换规则。作为最简单的非平凡应用，我们找到了与双引力子相关的参数化和对偶规则。此外，