arXiv 1708.010372017-08-03hep-th

全息术中的匹配重正化方案

Matching Renormalisation Schemes in Holography

Shinji Hirano

备注：: 12 pages

摘要：

在全息术中，体理论和边界理论中的物理观测量之间存在一一对应的关系。然而，为了定义物理可观测量，需要在对应的两边实现正则化。是否应该将对应关系扩展到常规意义上的非物理的正则化和重整化方案是可以理解的。然而，如果我们要认真对待全息的重正化群（RG）解释，它的精确理解似乎需要在体积和边界理论中匹配正则化和重正化方案。我们在AdS_5/CFT_4对应中解决了这个问题，通过考虑一个最简单的物理量，即R × S^3上N=4的超杨-米尔斯（SYM）理论的卡西米尔能量，在一个正则化函数中，并表明当截断保持有限时，有一些方案可以匹配AdS的整体结果，包括径向截断相关修正。我们进一步讨论了这一结果的RG解释全息的影响。

英文摘要：

In holography there is a one-to-one correspondence between physical observables in the bulk and boundary theories. To define physical observables, however, regularisation needs to be implemented in both sides of the correspondence. It is arguable whether the correspondence should extend to regularisation and renormalisation scheme which are not physical in the conventional sense. However, if we are to take the renormalisation group (RG) interpretation of holography seriously, its precise understanding appears to require the matching of regularisations and renormalisation schemes in the bulk and boundary theories. We address this question in the AdS_5/CFT_4 correspondence by considering a simplest physical quantity, the Casimir energy of the N=4 super Yang-Mills (SYM) theory on R x S^3, in a ζ-function regularisation and show that there are choices of scheme which match the bulk AdS result including the radial cutoff dependent corrections when the cutoff is kept finite. We further discuss the implication of this result to the RG interpretation of holography.

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