A toy model for the AdS/CFT correspondence

Berenstein, David

doi:10.1088/1126-6708/2004/07/018

Cited by 356 publications

(664 citation statements)

References 37 publications

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“…Further, these operators are a small fraction of the total number of operators with the correct quantum numbers to participate. This sheds some light on the important issue of decoupling a small set of nearly protected states [2], [19]. For the deformed theory, we proposed a set of operators dual to excited string modes, for large J.…”

Section: Discussionmentioning

confidence: 99%

“…This decoupling of a small set of nearly protected states has been used in both [2] and [19]. Understanding this decoupling directly in the relevant quantum field theory is an important problem.…”

Section: At Large N We Obtainmentioning

confidence: 99%

“…The analysis of this section provides some insight into this decoupling in the field theory. The usual argument [2], [19] involves taking a limit in which all states that are not nearly protected have a very large energy and hence decouple. In this subsection we have seen that, at this order in perturbation theory, the potential coupling between the nearly protected states and other states vanishes.…”

Section: At Large N We Obtainmentioning

confidence: 99%

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Deformed PP-waves from the Lunin-Maldacena background

Koch

Murugan

Smolic

et al. 2005

J. High Energy Phys.

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In this article we study a pp-wave limit of the Lunin-Maldacena background. We show that the relevant string theory background is a homogeneous ppwave. We obtain the string spectrum. The dual field theory is a deformation of N = 4 super Yang-Mills theory. We have shown that, for a class of operators, at O(g 2 Y M ) and at leading order in N, all contributions to the anomalous dimension come from F -terms. We are able to identify the operator in the deformed super Yang-Mills which is dual to the lowest string mode. By studying the undeformed theory we are able to provide some evidence, directly in the field theory, that a small set of nearly protected operators decouple. We make some comments on operators in the Yang-Mills theory that are dual to excited string modes.

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Section: Discussionmentioning

confidence: 99%

Section: At Large N We Obtainmentioning

confidence: 99%

Section: At Large N We Obtainmentioning

confidence: 99%

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Deformed PP-waves from the Lunin-Maldacena background

Koch

Murugan

Smolic

et al. 2005

J. High Energy Phys.

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“…The commutative ansatz (3.5) has been used before in ref. [2] to define a holomorphic normal matrix model. The above…”

Section: Non-commutative Solutions At Large Nmentioning

confidence: 99%

“…In ref. [2], Berenstein first proposed to consider a decoupled limit which singles out the half BPS sector in the N = 4 SYM. As a model for the dynamics of the half BPS states, he studied the gauged…”

Section: Introductionmentioning

confidence: 99%

BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography

Dai¹,

Wang²,

Wu³

2006

J. High Energy Phys.

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In this paper, we propose a new approach to study the BPS dynamics in N = 4 supersymmetric U(N ) Yang-Mills theory on R × S 3 , in order to better understand the emergence of gravity in the gauge theory. Our approach is based on supersymmetric, space-filling Q-balls with R-charge, which we call R-balls. The usual collective coordinate method for non-topological scalar solitons is applied to quantize the half and quarter BPS R-balls. In each case, a different quantization method is also applied to confirm the results from the collective coordinate quantization. For finite N , the half BPS R-balls with a U(1) R-charge have a moduli space which, upon quantization, results in the states of a quantum Hall droplet with filling factor ν = 1. These states are known to correspond to the "sources" in the Lin-Lunin-Maldacena geometries in IIB supergravity. For large N , we find a new class of quarter BPS R-balls with a non-commutativity parameter. Quantization on the moduli space of such R-balls gives rise to a non-commutative ChernSimons matrix mechanics, which is known to describe a fractional quantum Hall system. In view of AdS/CFT holography, this demonstrates a profound connection of emergent quantum gravity with non-commutative geometry, of which the quantum Hall effect is a special case.

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Chronology protection in AdS/CFT

Caldarelli

2006

Fortschritte der Physik

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We review the issue of chronology protection and show how string theory can solve it in the half BPS sector of AdS/CFT. According to the LLM prescription, half BPS excitations of AdS5 × S 5 geometries in type IIB string theory can be mapped into free fermion configurations. We show that unitarity of the theory describing these fermions is intimately related to the protection of the chronology in the dual geometries.Copyright line will be provided by the publisher The principle of causality stands at the foundation of all our understanding of physics. It cannot be relaxed without falling into paradoxes which, in the final analysis, consist either in the attempt to change the past conditions at the origin of the event or in the so-called bootstrap paradox, occurring when the effect is the cause of its own existence. The concept of causality is so important that it has been hardcoded into newtonian physics and special relativity. But as soon one takes into account the gravitational force, space and time become dynamical. Their evolution is driven by local equations and the equivalence principle ensures that the causality requirements of special relativity are locally respected. However, the gravitational field equations do not put any global constraint on the topology of time, leaving the possibility for the existence of closed timelike curves (CTCs), seeds of the violation of causality. The global nature of CTCs is what makes them so elusive and difficult to treat.Essentially, CTCs can arise by two mechanisms, rotation (or dragging of the inertial frames) and effectively superluminal propagation. The most well-known example of non topologically trivial CTCs induced by rotation is given by the Gödel universe [1], a homogeneous and simply connected manifold described by the metricHere, φ is a periodic angular coordinate, whose orbits become timelike for large r due to the framedragging term in the metric and form therefore CTCs. The fact that these CTCs exist at all times is a reason one can invoke to discard this solution. Another example is the Kerr black hole that has harmless CTCs induced by its rotation, but they are hidden by the Cauchy horizon, which is unstable. The situation is worse in higher dimensions, where naked CTCs are a generic feature of Kerr black holes [2]. It should be noted that supersymmetry does not help to rule out chronological pathologies [3], nor does the lifting to higher dimensional supergravities [4]. The other mechanism to create CTCs is to construct geometries allowing for effectively superluminal propagation of signals. For example, Gott's time machine [5] consists in two parallel cosmic strings in relative motion. The effect of the cosmic strings on the spacetime is to create conical defects, which can be cleverly exploited to build CTCs using the properties of Lorentz transformations (see figure 1). Again,

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A toy model for the AdS/CFT correspondence

Cited by 356 publications

References 37 publications

Deformed PP-waves from the Lunin-Maldacena background

Deformed PP-waves from the Lunin-Maldacena background

BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography

Chronology protection in AdS/CFT

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A toy model for the AdS/CFT correspondence

Cited by 356 publications

References 37 publications

Deformed PP-waves from the Lunin-Maldacena background

Deformed PP-waves from the Lunin-Maldacena background

BPSR-balls in Script N = 4 SYM onR×S3, quantum Hall analogy and AdS/CFT holography

Chronology protection in AdS/CFT

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Product

Resources

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BPSR-balls in Script N = 4 SYM onR×S³, quantum Hall analogy and AdS/CFT holography