We develop a general formalism of duality rotations for bosonic conformal spin-$s$ gauge fields, with $s\ge 2$, in a conformally flat four-dimensional spacetime. In the $s=1$ case, this formalism is equivalent to the theory of U(1) duality-invariant nonlinear electrodynamics developed by Gaillard and Zumino, Gibbons and Rasheed, and generalized by Ivanov and Zupnik. For each integer spin $s\ge 2$ we demonstrate the existence of families of conformal U(1) duality-invariant models, including a generalization of the so-called ModMax electrodynamics ($s=1$). Our bosonic results are then extended to the $\mathcal{N}=1$ and $\mathcal{N}=2$ supersymmetric cases. We also sketch a formalism of duality rotations for conformal gauge fields of Lorentz type $(m/2,n/2)$, for positive integers $m$ and $n$.

中文翻译：

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对偶不变超共形高自旋模型

我们开发了玻色共形自旋的二元旋转的一般形式$秒$ 规范场，与 $秒\ge 2$，在共形平坦的四维时空中。在里面$秒=1$在这种情况下，这种形式主义等价于由 Gaillard 和 Zumino、Gibbons 和 Rasheed 开发并由 Ivanov 和 Zupnik 推广的 U(1) 对偶不变非线性电动力学理论。对于每个整数自旋$秒\ge 2$ 我们证明了保形 U(1) 对偶不变模型族的存在，包括所谓的 ModMax 电动力学的推广（$秒=1$）。我们的玻色子结果然后扩展到$\mathcal{N}=1$ 和 $\mathcal{N}=2$超对称情况。我们还勾勒出洛伦兹型共形规范场的对偶旋转形式$(米/2,n/2)$, 对于正整数 $米$ 和 $n$.