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arXiv 1012.3382hep-th
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全息c定理与高阶导数引力

Holographic c-theorems and higher derivative gravity

James T. Liu, Wafic Sabra, Zhichen Zhao

摘要:

在AdS/CFT中,全息Weyl异常计算将a-异常系数与UV固定点处的体作用的性质相关联。这种普遍的行为表明了全息C-定理的可能性下流的IR。我们证明了这样一个C-定理更高的曲率洛夫洛克引力,在散装运动方程保持二阶。我们还探讨了f(R)引力作为一个玩具模型,其中无法避免更高的导数。在这种情况下,流动的单值性需要一个与理论的高阶导数性质有关的附加条件。这与f(R)黑洞熵的情况相反,在f(R)黑洞熵的情况下,第二定律是从完整的爱因斯坦方程和零能量条件的应用中得出的。

英文摘要:

In AdS/CFT, the holographic Weyl anomaly computation relates the a-anomaly coefficient to the properties of the bulk action at the UV fixed point. This universal behavior suggests the possibility of a holographic c-theorem for the a-anomaly under flows to the IR. We prove such a c-theorem for higher curvature Lovelock gravity, where the bulk equations of motion remain second order. We also explore f(R) gravity as a toy model where higher derivatives cannot be avoided. In this case, monoticity of the flow requires an additional condition related to the higher derivative nature of the theory. This is in contrast to the case of f(R) black hole entropy, where the second law follows from application of the full Einstein equations and the null energy condition.

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