In this note, we focus on the backreaction effects due to the chiral anomaly. The chiral anomaly modifies conserved currents, introducing new contributions. For Maxwell gauge fields, this leads to a contribution to the electric current proportional to the background magnetic field, a phenomenon known as the chiral magnetic effect, which is widely discussed in the literature. In the case of gravitational fields, as we demonstrate, the anomaly induces a new contribution to the stress-energy tensor. We analyze the potential manifestations of these modifications in the gravitational field and hydrodynamics in chiral media, and we also comment on backreaction effects in electrodynamics. In each case, we observe the systematic appearance of Beltrami-type fields. In electrodynamics and hydrodynamics, a Beltrami field (e.g., magnetic field or fluid velocity) is a vector parallel to its own curl. We propose a generalization of Beltrami fields for tensorial gravitational perturbations, calling the respective solutions to the gravitational equations gravitational spheromaks by analogy with a similar phenomenon in electrodynamics. In the modified hydrodynamics of chiral media, vorticity asymptotically forms a Beltrami vector field in a generalized Gromeka-Beltrami flow.

中文翻译：

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贝尔特拉米场、色散电磁波和手性异常的引力球体


在本说明中，我们重点介绍由手性异常引起的反向反应效应。手性异常改变了守恒电流，引入了新的贡献。对于麦克斯韦规范场，这会导致对电流的贡献与背景磁场成正比，这种现象称为手性磁效应，这在文献中得到了广泛讨论。正如我们所证明的，在引力场的情况下，这种异常会引起对应力-能量张量的新贡献。我们分析了这些修饰在引力场和手性介质中的流体动力学中的潜在表现，我们还评论了电动力学中的反反应效应。在每种情况下，我们都观察到 Beltrami 型场的系统外观。在电动力学和流体动力学中，贝尔特拉米场（例如磁场或流体速度）是平行于其自身旋度的矢量。我们提出了张量引力扰动的 Beltrami 场推广，通过与电动力学中的类似现象类比，将引力方程的相应解称为引力蝶形。在手性介质的修正流体动力学中，涡度在广义 Gromeka-Beltrami 流中渐近地形成 Beltrami 矢量场。