arXiv 2107.090522021-07-16hep-th

AdS/CFT Correspondence中的量子标量理论

Quantum Scalar Theories in the AdS/CFT Correspondence

Ernesto Bianchi

备注：: Master's thesis. 181 pages, 17 figures. Work in collaboration with Maximo Bañados, Ivan Muñoz and Kostas Skenderis. Comments are welcome

摘要：

本论文对AdS/CFT对应关系进行了创新性的研究。已知的是在经典近似下从这种对应产生的全息反射子，证实了这个水平上的猜想。在这项工作中，我们将探索它在这种近似之外的结果，考虑在固定的AdS（d+1）背景下标量Phi^3和Phi^4理论的特殊情况下，对这些已知的对偶双折射子的量子修正。这将涉及到一个计划的发展，系统地增加订单的量子修正经典获得的量子化与计算这些新的贡献，在路上引入合理的正则化和重整化方案的不同预期的分歧。这个过程将通过红外和紫外发散所起的主要作用清楚地显示这些环路校正的效果，简要总结如下：对全息反射器的量子校正以异常标度维度的形式在所得CFT中产生异常，证实了超越树级计算的猜想的有效性。所有这些研究都是在本论文中对理论参数的任意值进行的。为了研究本文的总体思路和结果，论文最后对一个具体的案例进行了分析。

英文摘要：

This thesis contains original research on the conjectured AdS/CFT correspondence. Known are the holographic correlators resulting from this correspondence under its classical approximation, confirming the conjecture at this level. In this work we will explore its consequences beyond this approximation, considering the quantum corrections to these known dual correlators for the particular cases of scalar Phi^3 and Phi^4 theories on a fixed AdS(d+1) background. This will involve the development of a scheme that adds systematically order by order the quantum corrections to the correlators obtained classically together with the computation of these new contributions, introducing on the way sensible regularization and renormalization schemes for the different expected divergences. This process will show in a clear way the effect of these loop corrections through the main role played by the infrared and ultraviolet divergences, which is briefly summarized in: the quantum corrections to the holographic correlators produce anomalies in the resulting CFT in the form of an anomalous scaling dimension, confirming the validity of the conjecture beyond tree-level computations. All this study is carried out throughout this thesis for arbitrary values of the parameters of the theory in the bulk. With the intention to study the general ideas and results developed in this work, at the end of the thesis a particular case is analyzed.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

摘要：

英文摘要：

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