Quantum Scalar Theories in the AdS/CFT Correspondence

TL;DR

This thesis investigates quantum corrections to holographic correlators in the AdS/CFT correspondence for scalar theories, demonstrating anomalies and confirming the conjecture beyond classical approximations.

Contribution

It develops a systematic scheme to compute quantum corrections to classical holographic correlators and analyzes their effects on the dual CFT, including anomalies and scaling dimensions.

Findings

Quantum corrections induce anomalies in the CFT.

The scheme systematically adds loop corrections to classical correlators.

Results confirm the AdS/CFT conjecture beyond tree-level.

Abstract

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.