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arXiv 1912.02597hep-th
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Ehlers作为双拷贝中的EM对偶

Ehlers as EM duality in the double copy

A. Banerjee, E. Ó Colgáin, J. A. Rosabal, H. Yavartanoo

备注：
v1 A short note describing the key observation of 1911.06797 in hopefully a simpler way; v2 Some meat added to the bones; v3 comments on the classical double copy interpretation of Einstein-Maxwell theory added, draft restructured to better highlight results; v4 matches published version
发表信息：
Phys. Rev. D 102, 126017 (2020)
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摘要：

给定具有等距方向的4D爱因斯坦重力解，已知运动方程与具有目标空间几何形状的3D $σ$模型的运动方程相同$SU(1,1)/U(1)$。因此，通过$SU(1, 1) \cong SL(2,\mathbb{R})$的任何变换都是作用的对称性，并且允许在4D中生成新的解。在这里，我们澄清和扩展最近的工作电磁（EM）对偶性的背景下，经典的双副本。特别是，对于纯引力，我们确定了一个明确的映射之间的麦克斯韦场的单副本和标量在目标空间中，使我们能够识别的$U(1) \subset SL(2, \mathbb{R})$对称双EM对偶的单副本。此外，我们扩展到Einstein-Maxwell理论的分析，在那里我们突出的作用，Ehlers-Harrison变换和球对称带电黑洞解，我们解释的运动方程作为一个截断的Einstein-Yang-Mills理论的假定单副本。

英文摘要：

Given a solution to 4D Einstein gravity with an isometry direction, it is known that the equations of motion are identical to those of a 3D $σ$-model with target space geometry $SU(1,1)/U(1)$. Thus, any transformation by $SU(1, 1) \cong SL(2,\mathbb{R})$ is a symmetry for the action and allows one to generate new solutions in 4D. Here we clarify and extend recent work on electromagnetic (EM) duality in the context of the classical double copy. In particular, for pure gravity, we identify an explicit map between the Maxwell field of the single copy and the scalars in the target space, allowing us to identify the $U(1) \subset SL(2, \mathbb{R})$ symmetry dual to EM duality in the single copy. Moreover, we extend the analysis to Einstein-Maxwell theory, where we highlight the role of Ehlers-Harrison transformations and, for spherically symmetric charged black hole solutions, we interpret the equations of motion as a truncation of the putative single copy for Einstein-Yang-Mills theory.

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