Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom
Effective metric Lagrangians from an underlying theory with two propagating degrees of freedom
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来自具有两个传播自由度的基础理论的有效度量拉格朗日量
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发表时间：
2009
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通讯作者：
K. Krasnov
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作者：
K. Krasnov
我们描述了一类无限参数的有效度量拉格朗日量，它产生于一个具有两个传播自由度的基础理论。拉格朗日量从爱因斯坦-希尔伯特项开始，接着是标准的R{sup 2}，（里奇）{sup 2}项，下一阶包含（黎曼）{sup 3}以及壳上消失项。这正是有效度量拉格朗日量的结构，它将两个环上的量子引力散度重新规范化。这表明，作为有效引力场论基础的理论可能没有比广义相对论所包含的更多的自由度。我们证明了有效度规理论可以只描述两个传播自由度的原因是存在一个（非局部）场重定义，它将无限复杂的有效度规拉格朗日映射到通常的爱因斯坦-希尔伯特。我们为我们的理论类描述这个映射，特别地，为（黎曼）{sup 3}项显式地展示它。
We describe an infinite-parametric class of effective metric Lagrangians that arise from an underlying theory with two propagating degrees of freedom. The Lagrangians start with the Einstein-Hilbert term, continue with the standard R{sup 2}, (Ricci){sup 2} terms, and in the next order contain (Riemann){sup 3} as well as on-shell vanishing terms. This is exactly the structure of the effective metric Lagrangian that renormalizes quantum gravity divergences at two loops. This shows that the theory underlying the effective field theory of gravity may have no more degrees of freedom than is already contained in general relativity. We show that the reason why an effective metric theory may describe just two propagating degrees of freedom is that there exists a (nonlocal) field redefinition that maps an infinitely complicated effective metric Lagrangian to the usual Einstein-Hilbert one. We describe this map for our class of theories and, in particular, exhibit it explicitly for the (Riemann){sup 3} term.