揭示与引力非最小耦合的 Proca 理论的不自洽性
Unveiling the inconsistency of the Proca theory with non-minimal coupling to gravity
AI总结：
针对与引力非最小耦合的 Proca 理论中纵向与张量模式看似同能标强耦合的问题，本文引入类似矢量型 disformal 变换的度规微扰耦合，消除非物理耦合，并构造不存在失控模式的 disformal 标架。
摘要：
我们研究了与引力非最小耦合的 Proca 理论的自由度。在 Minkowski 背景中，该理论传播五个自由度——一个有质量的纵向模式、两个有质量的矢量模式，以及两个无质量张量模式。乍看之下，度规微扰与矢量场之间的非线性耦合表明，纵向模式和张量模式都会在同一能标上变得强耦合。这将意味着，如果考虑非最小耦合，那么无论光子质量多小，引力波都必然是强耦合的。我们证明，摆脱这种不自洽性的途径是引入与度规微扰的 disformal 耦合，这种耦合类似于矢量型 disformal 变换。这样就可以避免两类模式之间非物理的耦合，从而使模型自洽。结果表明，只有纵向模式进入强耦合区，而张量模式和横向模式在直至 Planck 长度的所有能标上都保持弱耦合。最后，利用相同形式的 disformal 变换，我们引入了一个 disformal 标架，在该标架中，最近报道的失控模式不存在。
英文摘要：
We study the degrees of freedom of the Proca theory, non-minimally coupled to gravity. In the Minkowski background, this theory propagates five degrees of freedom -- a massive longitudinal mode, two massive vector ones, and two massless tensor modes. At first sight, the non-linear coupling between the metric perturbations and the vector field indicates that both longitudinal and tensor modes become strongly coupled, at the same scale. This would imply that no matter how small the photon mass is if non-minimal coupling is taken into account, gravitational waves would necessarily be strongly coupled. We show that the way out of this inconsistency is through the introduction of the disformal coupling to the metric perturbations that resemble the vector-type disformal transformations. This way, the unphysical coupling between the two types of modes can be avoided, rendering the model consistent. As a result, we show that only the longitudinal modes enter a strong coupling regime, while both tensor and transverse modes remain weakly coupled at all scales up to the Planck length. Finally, using the same form of the disformal transformation, we introduce a disformal frame in which the recently reported runaway modes are absent.
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