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arXiv 1907.09690hep-thgr-qchep-ph
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具有大质量自旋2和自旋0粒子的无鬼二次曲率理论

Ghostfree quadratic curvature theories with massive spin-2 and spin-0 particles

Katsuki Aoki, Shinji Mukohyama

备注：
17 pages, published version
发表信息：
Phys. Rev. D 100, 064061 (2019)
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摘要：

我们考虑了爱因斯坦引力的一般导数修正，并通过时空几何的扩展找到了在闵可夫斯基背景下没有鬼的新理论。我们假设黎曼-嘉当几何，即具有非零挠率的几何，并考虑拉格朗日量中所有可能的项，直到标度维度4。我们首先澄清的数量，自旋和奇偶性的所有粒子物种周围的闵可夫斯基背景，并发现其中一些粒子物种的幽灵一般的参数选择。另一方面，对于参数的特殊选择，那些可能的鬼变得无限重，因此可以从粒子种类的物理内容中去除。施加条件的耦合常数，以消除鬼，我们发现新的二次曲率理论，这是无鬼的闵可夫斯基背景的参数范围。这些理论的一个关键特征是在引力子传播子中存在一个非鬼质量自旋2粒子和一个非鬼质量自旋0粒子，以及无质量自旋2引力子。在挠率质量无限大的极限下，黎曼-嘉当几何退化为黎曼几何，粒子种类的物理内容与度规形式中著名的二次曲率理论一致，即有质量的自旋为2的鬼粒子、有质量的自旋为0的粒子和无质量的自旋为2的引力子。因此，除了其他约束外，鬼自由还设置了扭转质量的上限。除了上面提到的粒子种类，无鬼理论还包含一个质量自旋为1和一个质量自旋为0的粒子（第一类）或一对自旋为1的粒子（第二类）。这些额外的粒子种类通过物质场的自旋来调节重力。

英文摘要：

We consider generic derivative corrections to the Einstein gravity and find new classes of theories without ghost around the Minkowski background by means of an extension of the spacetime geometry. We assume the Riemann-Cartan geometry, i.e. a geometry with a non-vanishing torsion, and consider all possible terms in the Lagrangian up to scaling dimension four. We first clarify the number, spins, and parities of all particle species around the Minkowski background and find that some of those particle species are ghosts for generic choices of parameters. For special choices of the parameters, on the other hand, those would-be ghosts become infinitely heavy and thus can be removed from the physical content of particle species. Imposing the conditions on the coupling constants to eliminate the ghosts, we find new quadratic curvature theories which are ghost-free around the Minkowski background for a range of parameters. A key feature of these theories is that there exist a non-ghost massive spin-2 particle and a non-ghost massive spin-0 particle in the graviton propagator, as well as the massless spin-2 graviton. In the limit of the infinite mass of the torsion, the Riemann-Cartan geometry reduces to the Riemannian geometry and thus the physical content of particle species coincides with that of the well-known quadratic curvature theory in the metric formalism, i.e. a massive spin-2 ghost, a massive spin-0 particle and the massless spin-2 graviton. Ghost-freedom therefore sets, besides other constraints, an upper bound on the mass of the torsion. In addition to the above mentioned particle species, the ghost-free theory contains either the set of a massive spin-1 and a massive spin-0 (Class I) or a couple of spin-1 (Class II). These additional particle species mediate gravity sourced by the spin of matter fields.

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