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arXiv 1005.0619gr-qchep-th
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Action中的全息照相

Holography in Action

Sanved Kolekar, T. Padmanabhan

备注：
12 pages
发表信息：
Phys.Rev.D82:024036,2010
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摘要：

爱因斯坦-希尔伯特作用量和它在更高维度上的自然推广（如Lanczos-Lovelock作用量）具有某些特殊的特征。所有这些都可以分为体项和表面项，两者之间有特定的（"全息"）关系，因此任何一项都可以用来提取关于另一项的信息。此外，表面项导致壳层上视界的熵。过去有人认为，这些特征在传统方法中是不可能理解的，但如果我们将引力视为一种涌现现象，就会找到一种自然的解释。我们在本文中进一步支持这一观点。我们描述了一个替代的Einstein-Hilbert作用量和Lanczos-Lovelock作用量分解成一对新的表面项和体项，使得表面项成为视界上的Wald熵，体项是能量密度（这是爱因斯坦引力的ADM哈密顿密度）。我们表明，这种新的对也服从全息关系，并给出了热力学解释，在这种情况下，这种关系。由于在这种分解中，体项和表面项与能量和熵有关，所以全息条件可以被认为类似于将作为能量S = S（E，V）的函数给出的熵的表达式反转，以获得在正常热力学系统中的熵的能量E = E（S，V）。因此，作用的全息性质允许我们用两种不同的热力学势来描述同一系统。一些进一步可能的概括和影响进行了讨论。

英文摘要：

Einstein-Hilbert action and its natural generalizations to higher dimensions (like the Lanczos-Lovelock action) have certain peculiar features. All of them can be separated into a bulk and a surface term, with a specific ("holographic") relationship between the two, so that either term can be used to extract information about the other. Further, the surface term leads to entropy of the horizons on-shell. It has been argued in the past that these features are impossible to understand in the conventional approach but find a natural explanation if we consider gravity as an emergent phenomenon. We provide further support for this point of view in this paper. We describe an alternative decomposition of the Einstein-Hilbert action and Lanczos-Lovelock action into a new pair of surface and bulk terms, such that the surface term becomes Wald entropy on a horizon and the bulk term is the energy density (which is the ADM Hamiltonian density for Einstein gravity). We show that this new pair also obeys a holographic relationship and give a thermodynamic interpretation to this relation in this context. Since the bulk and surface terms, in this decomposition, are related to energy and entropy, the holographic condition can be thought of as analogous to inverting the expression for entropy given as a function of energy S = S(E,V) to obtain the energy E = E(S,V) in terms of the entropy in a normal thermodynamic system. Thus the holographic nature of the action allows us to relate the descriptions of the same system in terms of two different thermodynamic potentials. Some further possible generalizations and implications are discussed.

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