双度量模型的广义Weyl不变性与部分无质量
Extended Weyl Invariance in a Bimetric Model and Partial Masslessness
摘要：
我们重新审视一个特定的幽灵自由的双度量模型，这是有关的部分无质量（PM）和共形引力。线性地，该模型不仅在德西特周围，而且在平坦时空周围传播六个而不是七个自由度。非线性的运动方程可以用曲率幂展开的形式来改写，并且表现出相当多的结构。在这种形式中，方程被证明是不变的标量规范变换下，至少高达六阶导数，最低阶项是Weyl标度的度量。二阶导数项再现了德西特背景下通常的PM规范变换。在四阶导数阶，一个潜在的障碍，可能会破坏对称性消失。这反过来又保证了至少六阶导数的规范不变性。这相当于对共形引力加10阶导数修正。更一般地说，我们概述了一个程序，用于建设规范变换的顺序，作为一个扩展的衍生物和评论的有效性和局限性的程序。我们还讨论了最近的论点，反对存在的PM规范对称性在双度规理论，并表明，至少在其目前的形式，他们回避了这里考虑的模型。最后，我们认为，一个双度量的方法PM理论是更有前途的基础上存在的一个基本PM字段。
英文摘要：
We revisit a particular ghost-free bimetric model which is related to both partial masslessness (PM) and conformal gravity. Linearly, the model propagates six instead of seven degrees of freedom not only around de Sitter but also around flat spacetime. Nonlinearly, the equations of motion can be recast in the form of expansions in powers of curvatures, and exhibit a remarkable amount of structure. In this form, the equations are shown to be invariant under scalar gauge transformations, at least up to six orders in derivatives, the lowest order term being a Weyl scaling of the metrics. The terms at two-derivative order reproduce the usual PM gauge transformations on de Sitter backgrounds. At the four-derivative order, a potential obstruction that could destroy the symmetry is shown to vanish. This in turn guarantees the gauge invariance to at least six-orders in derivatives. This is equivalent to adding up to 10-derivative corrections to conformal gravity. More generally, we outline a procedure for constructing the gauge transformations order by order as an expansion in derivatives and comment on the validity and limitations of the procedure. We also discuss recent arguments against the existence of a PM gauge symmetry in bimetric theory and show that, at least in their present form, they are evaded by the model considered here. Finally, we argue that a bimetric approach to PM theory is more promising than one based on the existence of a fundamental PM field.
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