Rindler-AdS/CFT

In anti-de Sitter space a highly accelerating observer perceives a Rindler horizon. The two Rindler wedges in AdS_{d+1} are holographically dual to an entangled conformal field theory that lives on two boundaries with geometry R x H_{d-1}. For AdS_3, the holographic duality is especially tractable, allowing quantum-gravitational aspects of Rindler horizons to be probed. We recover the thermodynamics of Rindler-AdS space directly from the boundary conformal field theory. We derive the temperature from the two-point function and obtain the Rindler entropy density precisely, including numerical factors, using the Cardy formula. We also probe the causal structure of the spacetime, and find from the behavior of the one-point function that the CFT "knows" when a source has fallen across the Rindler horizon. This is so even though, from the bulk point of view, there are no local signifiers of the presence of the horizon. Finally, we discuss an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space.Comment: 29 Pages, 4 Figures, citations adde

Quantum scalar field theory in AdS and the AdS/CFT correspondence

In dieser Arbeit berechnen wir Quantenkorrekturen zu den Zwei- und Vierpunktsfunktionen bis zur zweiten Ordnung in der Kopplungskonstante für eine konform gekoppelte Skalarfeldtheorie mit quartischer Selbstwechselwirkung in der vierdimensionalen Anti–de Sitter-Raumzeit (AdS). Unsere Berechnungen werden durchgeführt, indem die übliche Feynman-Störungstheorie in flacher Raumzeit auf den Poincaré-Patch des Euklidischen AdS verallgemeinert wird. Insbesondere wenden wir keine Kenntnisse in konformer Feldtheorie (CFT) an. Die erhaltenen Ergebnisse für die Zwei- und Vierpunktsfunktionen sind miteinander konsistent. Darüber hinaus argumentieren wir, dass die kritischen Exponenten von Korrelationsfunktionen nahe des dreidimensionalen konformen Randes von AdS die erforderlichen Daten für die Renormierungsbedingungen liefern und somit die üblichen on-shell Bedingungen ersetzen. Die holographische Vierpunktsfunktion kann systematisch in den konformen Invarianten entwickelt und mit der konformen Block-Entwicklung auf dem Rand von AdS verglichen werden. Dies wird hier in niedriger Ordnung in den konformen Invarianten durchgeführt, wobei gezeigt wird, dass die entsprechenden Expansionskoeffizienten die Daten der konformen Block-Entwicklung eindeutig festlegen. Trotz Feinheiten bei UV- und (manchmal) IR-Divergenzen tritt kein Widerspruch auf. Wir zeigen ferner, dass die resultierende duale Randtheorie, stark eingeschränkt aufgrund der konformen Symmetrie und daher einer Reihe nichttrivialer Bedingungen unterliegend, tatsächlich eine mathematisch und physikalisch konsistente CFT ist. Unsere Theorie liefert daher eine erste explizite Bestätigung einer Quanten-AdS/CFT-Korrespondenz. Schließlich wird die Struktur der Operatorproduktentwicklung (OPE) der dualen CFT, einer deformierten verallgemeinerten freien Feldtheorie, zusammen mit den Korrekturen sowohl der OPE-Koeffizienten als auch der konformen Dimensionen der primären Operatoren dargelegt. Insbesondere wird das Fehlen des Energie-Impuls-Tensors und jeglicher erhaltener Ströme deutlich. Analytische Ausdrücke für die anomalen Dimensionen werden bei einer Loop-Ordnung gefunden, sowohl für Neumann- als auch für Dirichlet-Randbedingungen.In this thesis we compute quantum corrections to the two- and four-point correlation functions up to second order in the coupling constant for a conformally coupled scalar field theory with quartic selfinteraction in four-dimensional anti–de Sitter space-time (AdS). Our calculations are performed by generalizing the usual flat space-time Feynman perturbation theory to the Poincaré patch of Euclidean AdS. In particular, we do not exert any conformal field theory (CFT) knowledge. The obtained results for the two- and four-point functions are mutually consistent. In addition, we argue that the critical exponents of correlation functions near the three-dimensional conformal boundary of AdS provide the necessary data for the renormalization conditions, thus replacing the usual on-shell condition. The holographic four-point function can systematically be expanded in the conformal invariants and compared with the conformal block expansion on the boundary of AdS. This is carried out here at low order in the conformal invariants, where the corresponding expansion coefficients are shown to uniquely fix the data for the conformal block expansion. No contradiction arises despite subtleties with UV and (sometimes) IR divergences. We also show that the disclosed boundary dual, subject to a set of nontrivial conditions dictated by the strong constraint of conformal symmetry, is indeed a mathematically and physically consistent CFT. Hence, our theory provides a first explicit confirmation of a quantum AdS/CFT correspondence. Finally, the operator product expansion (OPE) structure of the dual CFT, a deformed generalized free field theory, is revealed, along with the corrections to both the OPE coefficients and conformal dimensions of primary operators. In particular, the absence of the stress tensor and of any conserved current becomes explicit. Analytic expressions for the anomalous dimensions are found at one loop, both for Neumann and Dirichlet boundary conditions

Holography in Rindler Space

abstract: This thesis addresses certain quantum aspects of the event horizon using the AdS/CFT correspondence. This correspondence is profound since it describes a quantum theory of gravity in d + 1 dimensions from the perspective of a dual quantum field theory living in d dimensions. We begin by considering Rindler space which is the part of Minkowski space seen by an observer with a constant proper acceleration. Because it has an event horizon, Rindler space has been studied in great detail within the context of quantum field theory. However, a quantum gravitational treatment of Rindler space is handicapped by the fact that quantum gravity in flat space is poorly understood. By contrast, quantum gravity in anti-de Sitter space (AdS), is relatively well understood via the AdS/CFT correspondence. Taking this cue, we construct Rindler coordinates for AdS (Rindler-AdS space) in d + 1 spacetime dimensions. In three spacetime dimensions, we find novel one-parameter families of stationary vacua labeled by a rotation parameter β. The interesting thing about these rotating Rindler-AdS spaces is that they possess an observer-dependent ergoregion in addition to having an event horizon. Turning next to the application of AdS/CFT correspondence to Rindler-AdS space, we posit that the two Rindler wedges in AdSd+1 are dual to an entangled conformal field theory (CFT) that lives on two boundaries with geometry R × Hd-1. Specializing to three spacetime dimensions, we derive the thermodynamics of Rindler-AdS space using the boundary CFT. We then probe the causal structure of the spacetime by sending in a time-like source and observe that the CFT “knows” when the source has fallen past the Rindler horizon. We conclude by proposing an alternate foliation of Rindler-AdS which is dual to a CFT living in de Sitter space. Towards the end, we consider the concept of weak measurements in quantum mechanics, wherein the measuring instrument is weakly coupled to the system being measured. We consider such measurements in the context of two examples, viz. the decay of an excited atom, and the tunneling of a particle trapped in a well, and discuss the salient features of such measurements.Dissertation/ThesisPh.D. Physics 201

Light-front holographic QCD and emerging confinement

In this report we explore the remarkable connections between light-front dynamics, its holographic mapping to gravity in a higher-dimensional anti-de Sitter (AdS) space, and conformal quantum mechanics. This approach provides new insights into the origin of a fundamental mass scale and the physics underlying confinement dynamics in QCD in the limit of massless quarks. The result is a relativistic light-front wave equation for arbitrary spin with an effective confinement potential derived from a conformal action and its embedding in AdS space. This equation allows for the computation of essential features of hadron spectra in terms of a single scale. The light-front holographic methods described here give a precise interpretation of holographic variables and quantities in AdS space in terms of light-front variables and quantum numbers. This leads to a relation between the AdS wave functions and the boost-invariant light-front wave functions describing the internal structure of hadronic bound-states in physical space-time. The pion is massless in the chiral limit and the excitation spectra of relativistic light-quark meson and baryon bound states lie on linear Regge trajectories with identical slopes in the radial and orbital quantum numbers. In the light-front holographic approach described here currents are expressed as an infinite sum of poles, and form factors as a product of poles. At large q(2) the form factor incorporates the correct power-law fall-off for hard scattering independent of the specific dynamics and is dictated by the twist. At low q2 the form factor leads to vector dominance. The approach is also extended to include small quark masses. We briefly review in this report other holographic approaches to QCD, in particular top-down and bottom-up models based on chiral symmetry breaking. We also include a discussion of open problems and future applications. (C)) 2015 Elsevier B.V. All rights reserved

Holography of the BTZ Black Hole, Inside and Out

We propose a 1+1 dimensional CFT dual structure for quantum gravity and matter on the extended 2+1 dimensional BTZ black hole, realized as a quotient of the Poincare patch of AdS$_3$. The quotient spacetime includes regions beyond the singularity, "whiskers", containing timelike and lightlike closed curves, which at first sight seem unphysical. The spacetime includes the usual AdS-asymptotic boundaries outside the horizons as well as boundary components inside the whiskers. We show that local boundary correlators with some endpoints in the whisker regions: (i) are a protected class of amplitudes, dominated by effective field theory even when the associated Witten diagrams appear to traverse the singularity, (ii) describe well-defined diffeomorphism-invariant quantum gravity amplitudes in BTZ, (iii) sharply probe some of the physics inside the horizon but outside the singularity, and (iv) are equivalent to correlators of specific non-local CFT operators in the standard thermofield entangled state of two CFTs. In this sense, the whisker regions can be considered as purely auxiliary spacetimes in which these useful non-local CFT correlators can be rendered as local boundary correlators, and their diagnostic value more readily understood. Our results follow by first performing a novel reanalysis of the Rindler view of standard AdS/CFT duality on the Poincare patch of AdS, followed by exploiting the simple quotient structure of BTZ which turns the Rindler horizon into the BTZ black hole horizon. While most of our checks are within gravitational effective field theory, we arrive at a fully non-perturbative CFT proposal to probe the UV-sensitive approach to the singularity.Comment: 52 pages, 15 figures. v2: Clarifications made throughout paper. Derivation of (new) Section 8 corrected. Results and conclusions unchanged. References adde

Non perturbative instabilities of Anti-de Sitter solutions to M-theory

Ooguri and Vafa have recently conjectured that in a consistent theory of quantum gravity, all non supersymmetric Anti-de Sitter solutions supported by fluxes must be unstable. Whenever the solution is perturbatively stable, it is interesting to investigate possible non perturbative mechanisms leading to instabilities. A prototypical such mechanism is provided by Witten’s bubble of nothing, which demonstrates the instability of the Kaluza-Klein vacuum. The thesis aims at testing further the Ooguri-Vafa conjecture by studying generalizations of Witten's solution in the context of M-theory compactifications