质量/电荷与 NUT/磁荷：$D\geq4$ 中所有玻色子自旋的散射振幅对偶性
Mass/electric versus NUT/magnetic charges: duality from scattering amplitudes in $D\geq4$ and for all bosonic spins
AI总结：
研究 $D\geq4$ 中 Kerr-NUT 度规及相关自旋 - $s$ 场的散射振幅，通过旋转变形径向方程关联质量、NUT 电荷等，建立高维‘电磁’对偶性，由三点散射振幅揭示，探讨自对偶性，未发现 $D = 4$ 自对偶引力可积性的高维类似证据。
AI中文摘要：
我们重新审视了 $D\geq4$ 中的 Kerr-NUT 度规及相关自旋 - $s$ 场，并研究其相关散射振幅。从位置空间出发，我们强调质量和（多个）NUT 电荷与旋转变形径向方程不同解的关联，在笛卡尔多 Kerr - Schild 坐标中得以明确。此解释扩展到带磁荷的电磁学及高自旋对应情形。接着在高维建立了‘电磁’对偶性，将质量/电荷与 NUT/磁荷关联，以新方式推广了 $D = 4$ 的情形。对于 $D\geq6$，涉及多磁荷相等的选择。对偶性在动量空间由生成解的三点散射振幅揭示。所有自旋的这些振幅由自旋提升算符 $\mathcal S_\mu$ 构建，作用于标量种子。电扇区的标量种子与磁扇区对偶，前者旋转依赖求和为贝塞尔函数 $J_{\frac{D - 5}{2}}$，后者为 $J_{-\frac{D - 5}{2}}$。最后探讨了由此产生的自对偶性概念，研究决定主导阶散射的经典 $2\!\mapsto\!2$ 振幅，未发现 $D = 4$ 自对偶引力可积性的高维类似证据。
英文摘要：
We revisit Kerr-NUT metrics and related spin-$s$ fields in $D\geq4$, and study their associated scattering amplitudes. Starting in position space, we highlight the interpretation of mass and (multiple) NUT charges as being associated to distinct solutions of the rotation-deformed radial equation, which is made explicit in Cartesian multi-Kerr-Schild coordinates. This interpretation extends to electromagnetism with magnetic-type charges, and also extends to higher-spin counterparts, in accordance with the classical double or multi copy. We then establish a notion of ``electric-magnetic" duality in higher dimensions, relating mass/electric to NUT/magnetic charges, which generalises the $D=4$ case in a novel manner. For $D\geq6$, this involves the choice where the multiple magnetic charges are equal. The duality is revealed in momentum space, by the 3-point scattering amplitudes that generate the solutions. For all spins, these amplitudes are constructed from a spin-raising operator $\mathcal S_μ$ and take the form $\varepsilon^{μ_1\cdotsμ_s}{\mathcal S}_{μ_1}\cdots {\mathcal S}_{μ_s}$ acting on a scalar seed. The scalar seed of the electric sector is dual to that of the magnetic sector: where the former's rotation dependence resums to a Bessel function $J_{\frac{D-5}{2}}$, the latter resums to a Bessel function $J_{-\frac{D-5}{2}}$. Finally, we explore the notion of self-duality that arises from this picture. Studying the classical $2\!\mapsto\!2$ amplitudes that determine leading-order scattering, we find no evidence of a higher-dimensional analogue of the integrability of $D=4$ self-dual gravity.
