arXiv 2307.047482023-07hep-th

一般时空中自对偶p形式规范场的协变作用量

Covariant Action for Self-Dual p-Form Gauge Fields in General Spacetimes

C. M. Hull

备注：: 77 pages. Additional material on interactions added

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AI总结：

本文提出Sen作用量的协变推广，用第二度规替代Minkowski度规，实现自对偶p形式规范场在任意时空的协变描述，并引入退耦的影子扇区及两类对称性。

摘要：

Sen关于自对偶场强与时空度规g耦合的p形式规范场的作用量涉及显式的Minkowski度规，这一存在引发了关于该作用量是否坐标无关以及能否在一般时空流形上使用的疑问。本文提出了Sen作用量的一种自然推广，其中Minkowski度规被时空上的第二个度规\ar g所取代。该理论是协变的，可在任意时空上表述。该理论描述一个物理扇区，由与动力学度规g耦合的手征p形式规范场组成，外加一个由第二个手征p形式和第二个度规\ar g组成的影子扇区。影子扇区中的场仅彼此耦合，与物理扇区无相互作用，因此从物理扇区退耦。所得理论是协变的，可在任意时空上表述。文中给出了相互作用的显式表达式，并提供了包含与其他物理场相互作用或高阶导数场方程的扩展。具有两个度规的时空具有一些有趣的几何性质，本文对此进行了部分探索，并将其用于相互作用的构造。该作用量具有两个类微分同胚对称性，一个仅作用于物理扇区，另一个仅作用于影子扇区，时空微分同胚对称性作为对角子群出现。这允许进一步的推广，其中\ar g不是张量场，而是规范场，其跃迁函数涉及通常的坐标变换以及影子扇区规范变换。

英文摘要：

Sen's action for a $p$-form gauge field with self-dual field strength coupled to a spacetime metric $g$ involves an explicit Minkowski metric and the presence of this raises questions as to whether the action is coordinate independent and whether it can be used on a general spacetime manifold. A natural generalisation of Sen's action is presented in which the Minkowski metric is replaced by a second metric $\bar g$ on spacetime. The theory is covariant and can be formulated on any spacetime. The theory describes a physical sector, consisting of the chiral $p$-form gauge field coupled to the dynamical metric $g$, plus a shadow sector consisting of a second chiral $p$-form and the second metric $\bar g$. The fields in this shadow sector only couple to each other and have no interactions with the physical sector, so that they decouple from the physical sector. The resulting theory is covariant and can be formulated on any spacetime. Explicit expressions are found for the interactions and extensions to include interactions with other physical fields or higher-derivative field equations are given. A spacetime with two metrics has some interesting geometry and some of this is explored here and used in the construction of the interactions.The action has two diffeomorphism-like symmetries, one acting only on the physical sector and one acting only on the shadow sector, with the spacetime diffeomorphism symmetry arising as the diagonal subgroup. This allows a further generalisation in which $\bar g$ is not a tensor field but is instead a gauge field whose transition functions involve the usual coordinate transformation together with a shadow sector gauge transformation.

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