What Do CFTs Tell Us About Anti-de Sitter Spacetimes?

This paper reviews advances in the understanding of quantum gravity based on field theory calculations in the AdS/CFT correspondence.

We argue that a non-perturbative description of quantum gravity should involve two (non-interacting) copies of a dual field theory on the boundary, and describe the states of the spacetimes accordingly. So, for instance, a complete description of the asymptotically Anti-de-Sitter spacetimes is given by two copies of the conformal field theory associated to the global AdS spacetime. We also argue that, in this context, gravitational collapse and formation of a black hole may b...

In this thesis we apply techniques from quantum information theory to study quantum gravity within the framework of the anti-de Sitter / conformal field theory correspondence (AdS/CFT). Through AdS/CFT, progress has been made in understanding the structure of entanglement in quantum field theories, and in how gravitational physics can emerge from these structures. However, this understanding is far from complete and will require the development of new tools to quantify correl...

Considering theories in sectors of large global charge $Q$ results in a semiclassical effective field theory (EFT) description for some strongly-coupled conformal field theories (CFTs) with continuous global symmetries. Hence, when studying dualities at large charge, we can have control over the strongly coupled side of the duality and gain perturbative access to both dual pairs. In this work we discuss the AdS/CFT correspondence in the regime $Q \gg C_T \gg 1$ where both the...

We introduce the AdS/CFT correspondence as a natural extension of QFT in a fixed AdS background. We start by reviewing some general concepts of CFT, including the embedding space formalism. We then consider QFT in a fixed AdS background and show that one can define boundary operators that enjoy very similar properties as in a CFT, except for the lack of a stress tensor. Including a dynamical metric in AdS generates a boundary stress tensor and completes the CFT axioms. We als...

An S-matrix analog is defined for anti-de Sitter space by constructing ``in'' and ``out'' states that asymptote to the timelike boundary. A derivation parallel to that of the LSZ formula shows that this ``boundary S-matrix'' is given directly by correlation functions in the boundary conformal theory. This provides a key entry in the AdS to CFT dictionary.

By using the approach of non-commutative geometry, we study spinors and scalars on the two layers AdS$_{d+1}$ space. We have found that in the boundary of two layers AdS$_{d+1}$ space, by using the AdS/CFT correspondence, we have a logarithmic conformal field theory. This observation propose a way to get the quantum field theory in the context of non-commutative geometry.

Light-cone form of field dynamics in anti-de Sitter space-time is developed. Using field theoretic and group theoretic approaches the light-cone representation for generators of anti-de Sitter algebra acting as differential operators on bulk fields is found. We also present light-cone reformulation of the boundary conformal field theory representations. Making use of these explicit representations of AdS algebra as isometry algebra in the bulk and the algebra of conformal tra...

A consistent QM/NCG duality is put forward as a model for the AdS^2/CFT_1 correspondence. This is a duality/correspondence between 1) the dAFF conformal quantum mechanics (QM) on the boundary (which is only "quasi-conformal" in the sense that there is neither an SO(1,2)-invariant vacuum state nor there are strictly speaking primary operators), and between 2) the noncommutative geometry of AdS^2_{\theta} in the bulk (which is only "quasi-AdS" in the sense of being only asympto...

In this paper we discuss the dynamics of conformal field theories on anti-de Sitter space, focussing on the special case of the N=4 supersymmetric Yang-Mills theory on AdS_4. We argue that the choice of boundary conditions, in particular for the gauge field, has a large effect on the dynamics. For example, for weak coupling, one of two natural choices of boundary conditions for the gauge field leads to a large N deconfinement phase transition as a function of the temperature,...