arXiv 0907.50092009-07hep-th

$D=2+1$中一个新的自旋2自对偶模型

A new spin-2 self-dual model in $D=2+1$

D. Dalmazi, E. L. Mendonca

备注：: 14 pages, no figures, typos fixed, reference (19) modified
发表信息：: JHEP 0909:011,2009
DOI：: 10.1088/1126-6708/2009/09/011

摘要：

在$D=2+1$中有三种螺旋度为+2（或-2）的大质量粒子的自对偶模型。每个模型都是一阶、二阶和三阶导数。在这里，我们得到一个新的自对偶模型的四阶，$\cL {SD}^{(4)}$，它遵循三阶模型（线性化拓扑质量引力）通过Noether嵌入的线性化Weyl对称性。事实上，每一个自对偶模型都可以从前一个$ \cL {SD}^{(i)} \to \cL {SD}^{(i+1)}, i=1,2,3$通过适当规范对称性的Noether嵌入得到，最终得到$\cL {SD}^{(4)}$。新模型可以用线性化版本的$\cL {HDTMG} = ε^{μνρ} Γ_{μγ}^ε(\p_νΓ_{ερ}^γ+ (2/3)Γ_{νδ}^γΓ_{ρε}^δ) /8 m + \sqrt{-g}(R_{μν} R^{νμ} - 3 R^2/8) /2 m^2 $来识别。我们还构建了一个主行动有关的三阶自对偶模型$\cL {SD}^{(4)}$的混合项没有粒子的内容，确保频谱等价的$\cL {SD}^{(4)}$其他低阶自对偶模型，尽管其纯高阶导数性质和爱因斯坦-希尔伯特行动的情况下。$\cL {SD}^{(4)}$的相关自由度被编码在秩2张量中，该秩2张量由于平凡（非动力学）恒等式而对称、无迹和横向，与其他自旋2自对偶模型相反。我们还证明了Fierz-Pauli理论的Noether嵌入导致了Bergshoeff，Hohm和Townsend的新的大质量引力。

英文摘要：

There are three self-dual models of massive particles of helicity +2 (or -2) in $D=2+1$. Each model is of first, second, and third-order in derivatives. Here we derive a new self-dual model of fourth-order, $\cL {SD}^{(4)}$, which follows from the third-order model (linearized topologically massive gravity) via Noether embedment of the linearized Weyl symmetry. In fact, each self-dual model can be obtained from the previous one $ \cL {SD}^{(i)} \to \cL {SD}^{(i+1)}, i=1,2,3$ by the Noether embedment of an appropriate gauge symmetry, culminating in $\cL {SD}^{(4)}$. The new model may be identified with the linearized version of $\cL {HDTMG} = ε^{μνρ} Γ_{μγ}^ε(\p_νΓ_{ερ}^γ+ (2/3)Γ_{νδ}^γΓ_{ρε}^δ) /8 m + \sqrt{-g}(R_{μν} R^{νμ} - 3 R^2/8) /2 m^2 $. We also construct a master action relating the third-order self-dual model to $\cL {SD}^{(4)}$ by means of a mixing term with no particle content which assures spectrum equivalence of $\cL {SD}^{(4)}$ to other lower-order self-dual models despite its pure higher derivative nature and the absence of the Einstein-Hilbert action. The relevant degrees of freedom of $\cL {SD}^{(4)}$ are encoded in a rank-two tensor which is symmetric, traceless and transverse due to trivial (non-dynamic) identities, contrary to other spin-2 self-dual models. We also show that the Noether embedment of the Fierz-Pauli theory leads to the new massive gravity of Bergshoeff, Hohm and Townsend.

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