arXiv 2303.026162023-03hep-th

自由场的对偶化

Dualisation of free fields

V. A. Abakumova, S. L. Lyakhovich

备注：: 31 pages, minor corrections
DOI：: 10.1016/j.aop.2023.169322

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AI总结：

研究包含拓扑子系统的自由场理论，提出通过母作用量在对偶表述间切换的一般对偶化程序，并以无质量和有质量自旋2场为例说明。

摘要：

我们考虑一般的自由场理论，使得运动方程系统包含一个具有特殊性质的子系统。如果单独考虑该子系统，它将是一个没有局部自由度的拓扑场论。各种著名的场论都包含这样的子系统，包括 Einstein 引力。由于该子系统是拓扑理论，其通解是纯规范（除去全局自由度）。线性理论子系统的规范对称性可以被显式求出，从而提供该子系统的通解。将此解代入整个系统，我们得到一个等价的场论，其中场变量的角色由拓扑子系统的规范参数扮演。这些场可被视为原始场的势。我们提出了一个构造“母作用量”的一般程序，该作用量包含两种对偶表述的场。在该作用量层面，可以通过施加适当的规范固定条件在对偶表述之间切换。这一一般对偶化程序以无质量和有质量的自旋为 2 的场为例进行了说明。对于无质量情况，hook 型张量作为度规的势，而对于有质量情况，则是具有窗口 Young 图的四阶张量。

英文摘要：

We consider the general free field theory such that system of equations of motion includes a subsystem with a special property. If the subsystem is considered by itself, it would be a topological field theory having no local degrees of freedom. Various well-known field theories admit such a subsystem, including Einstein's gravity. As the subsystem is a topological theory, the general solution is a pure gauge, modulo global degrees of freedom. Gauge symmetry of the subsystem of linear theory can be explicitly found, providing the general solution to the subsystem. Substituting this solution into entire system, we arrive at an equivalent field theory where the role of the field variables is played by the gauge parameters of the topological subsystem. These fields can be viewed as the potentials for the original ones. A general procedure is proposed for constructing a "parent action" which includes the fields of both dual formulations. At the level of this action, one can switch between dual formulations by imposing appropriate gauge fixing conditions. This general dualisation procedure is exemplified by massless and massive spin two fields. For the massless case, the hook type tensor serves as a potential for the metric, while for the massive case it is the fourth rank tensor with window Young diagram.

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