Chronology protection in AdS/CFT

Abstract

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,

Holographic dual of a time machine

“…An intriguing observation has been made by the authors of [25] and [26], that from the point of view of the AdS/CFT correspondence, the existence of CTC in the bulk can be related to negative or exceeding one fermionic probability in the boundary field theory. Per contra, in [27] it was demonstrated that, by deforming AdS 5 × S 5 spacetime in a certain way, it is possible to construct a supergravity solution possessing CTC confined to the bulk, such that the stress-energy tensor of the dual boundary N ¼ 4 superYang-Mills theory remains well defined and finite.…”

“…In this paper we address this problem and by use of the AdS/CFT correspondence provide a constructive solution to it. Here we stand on the position that even if the presence of CTC causes breaking of unitarity in the boundary field theory [26], it should not be regarded as a big problem as long as we can formulate a prescription how to solve the theory. When one is trying to get an insight into physics of paradoxical systems, it is not very useful to rely on the "common sense" intuition and corresponding fundamental principles.…”

“…Thus the chronology is protected, but structure of the CTC remains unbroken by quantum effects. An intriguing observation has been made by authors of [21] and [22], that from the point of view of the AdS/CFT correspondence, the existence of CTC in the bulk can be related to negative or exceeding one fermionic probability in the boundary field theory.…”