标题： 关于非洛伦兹对偶对称性的一篇笔记 显示英文标题

标题： A note on non-Lorentzian duality symmetries

摘要： 我们推导出了电磁学和线性化引力的非洛伦兹对偶作用量，在卡洛里安和伽利略两种情况下均适用。 与洛伦兹理论的情况一样，这是通过首先构造一个母作用量来实现的，该母作用量可以约化为一对对偶作用量。 对于麦克斯韦理论而言，每一对对偶作用量由原始理论已知的“电”极限和“磁”极限组成，表明这些极限之间存在一种场外电磁对偶关系。 我们得到了如下双重性：一方面，线性化引力的二阶非洛伦兹收缩；另一方面，通过规范对应的动力学代数所得到的理论之间的对偶性。 在卡洛里安收缩的情况下，这些对偶作用量重现了已知的卡洛里安引力的“电”和“磁”理论，并且我们在伽利略情况下发现了类似的结果。 显示英文摘要

摘要： We work out non-Lorentzian dual actions for electromagnetism and linearised gravity, both in the Carrollian and Galilean cases. This is done in the same way as for Lorentzian theories, by first constructing a parent action that reduces to a pair of dual actions. In the case of Maxwell theory, each pair of dual actions consists of the known `electric' and `magnetic' limits of the original theories, showing that these limits are related by an off-shell electromagnetic duality. We have obtained dualities between on one hand the non-Lorentzian contractions of linearised gravity in second-order form, and on the other hand the theories one obtains by gauging the corresponding kinematic algebras. In the Carrollian contraction, these dual actions reproduce the known `electric' and `magnetic' Carrollian theories of gravity, and we find a similar result in the Galilean case.