Author
Ben Craps
Other affiliations: Katholieke Universiteit Leuven, University of Amsterdam, École Normale Supérieure ...read more
Bio: Ben Craps is an academic researcher from Vrije Universiteit Brussel. The author has contributed to research in topics: Gravitational singularity & String theory. The author has an hindex of 39, co-authored 143 publications receiving 4868 citations. Previous affiliations of Ben Craps include Katholieke Universiteit Leuven & University of Amsterdam.
Papers published on a yearly basis
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TL;DR: Using the holographic mapping to a gravity dual, 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 are calculated to probe the scale dependence of thermalization following a sudden injection of energy.
Abstract: Using the holographic mapping to a gravity dual, we calculate 2-point functions, Wilson loops, and entanglement entropy in strongly coupled field theories in d=2, 3, and 4 to probe the scale dependence of thermalization following a sudden injection of energy. For homogeneous initial conditions, the entanglement entropy thermalizes slowest and sets a time scale for equilibration that saturates a causality bound. The growth rate of entanglement entropy density is nearly volume-independent for small volumes but slows for larger volumes. In this setting, the UV thermalizes first.
425 citations
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TL;DR: In this article, a model for a big bang type singularity in string theory/M-theory was proposed. But the model is based on a (1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given by the Milne orbifold of (1 + 1)-d Minkowski space.
Abstract: The light-like linear dilaton background represents a particularly simple time-dependent 1/2 BPS solution of critical type-IIA superstring theory in ten dimensions. Its lift to M-theory, as well as its Einstein frame metric, are singular in the sense that the geometry is geodesically incomplete and the Riemann tensor diverges along a light-like subspace of codimension one. We study this background as a model for a big bang type singularity in string theory/M-theory. We construct the dual Matrix theory description in terms of a (1+1)-d supersymmetric Yang-Mills theory on a time-dependent world-sheet given by the Milne orbifold of (1+1)-d Minkowski space. Our model provides a framework in which the physics of the singularity appears to be under control.
208 citations
TL;DR: In this article, the scale dependence of thermalization in strongly coupled field theories following a quench was investigated using the AdS/CFT correspondence, via calculations of two-point functions, Wilson loops and entanglement entropy in d = 2,3,4.
Abstract: Using the AdS/CFT correspondence, we probe the scale-dependence of thermalization in strongly coupled field theories following a quench, via calculations of two-point functions, Wilson loops and entanglement entropy in d=2,3,4 In the saddlepoint approximation these probes are computed in AdS space in terms of invariant geometric objects - geodesics, minimal surfaces and minimal volumes Our calculations for two-dimensional field theories are analytical In our strongly coupled setting, all probes in all dimensions share certain universal features in their thermalization: (1) a slight delay in the onset of thermalization, (2) an apparent non-analyticity at the endpoint of thermalization, (3) top-down thermalization where the UV thermalizes first For homogeneous initial conditions the entanglement entropy thermalizes slowest, and sets a timescale for equilibration that saturates a causality bound over the range of scales studied The growth rate of entanglement entropy density is nearly volume-independent for small volumes, but slows for larger volumes
207 citations
TL;DR: In this article, the authors show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry.
Abstract: The scalars in vector multiplets of N=2 supersymmetric theories in 4 dimensions exhibit `special Kaehler geometry', related to duality symmetries, due to their coupling to the vectors. In the literature there is some confusion on the definition of special geometry. We show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kaehler metric to one that occurs in N=2 supersymmetry. We treat the rigid as well as the local supersymmetry case. The connection is made to moduli spaces of Riemann surfaces and Calabi-Yau 3-folds. The conditions for the existence of a prepotential translate to a condition on the choice of canonical basis of cycles.
166 citations
TL;DR: In this paper, the authors show equivalences of some definitions and give examples which show that earlier definitions are not equivalent, and are not sufficient to restrict the Kahler metric to one that occurs in N = 2 supersymmetry.
161 citations
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TL;DR: In this paper, the holographic correspondence between field theories and string/M theory is discussed, focusing on the relation between compactifications of string theory on anti-de Sitter spaces and conformal field theories.
5,610 citations
TL;DR: In this article, the authors used holography to study sensitive dependence on initial conditions in strongly coupled field theories and showed that the effect of the early infalling quanta relative to the t = 0 slice creates a shock wave that destroys the local two-sided correlations present in the unperturbed state.
Abstract: We use holography to study sensitive dependence on initial conditions in strongly coupled field theories. Specifically, we mildly perturb a thermofield double state by adding a small number of quanta on one side. If these quanta are released a scrambling time in the past, they destroy the local two-sided correlations present in the unperturbed state. The corresponding bulk geometry is a two-sided AdS black hole, and the key effect is the blueshift of the early infalling quanta relative to the t = 0 slice, creating a shock wave. We comment on string- and Planck-scale corrections to this setup, and discuss points that may be relevant to the firewall controversy.
1,589 citations
01 Jun 1993
TL;DR: In this paper, it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature, which leads to a slow decrease in the mass of the black hole and to its eventual disappearance.
Abstract: In the classical theory black holes can only absorb and not emit particles. However it is shown that quantum mechanical effects cause black holes to create and emit particles as if they were hot bodies with temperature\(\frac{{h\kappa }}{{2\pi k}} \approx 10^{ - 6} \left( {\frac{{M_ \odot }}{M}} \right){}^ \circ K\) where κ is the surface gravity of the black hole. This thermal emission leads to a slow decrease in the mass of the black hole and to its eventual disappearance: any primordial black hole of mass less than about 1015 g would have evaporated by now. Although these quantum effects violate the classical law that the area of the event horizon of a black hole cannot decrease, there remains a Generalized Second Law:S+1/4A never decreases whereS is the entropy of matter outside black holes andA is the sum of the surface areas of the event horizons. This shows that gravitational collapse converts the baryons and leptons in the collapsing body into entropy. It is tempting to speculate that this might be the reason why the Universe contains so much entropy per baryon.
1,009 citations
TL;DR: In this paper, the authors compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states, and match the bulk and boundary computations of the entropy in the case of a two-dimensional CFT.
Abstract: We compute the time-dependent entanglement entropy of a CFT which starts in relatively simple initial states. The initial states are the thermofield double for thermal states, dual to eternal black holes, and a particular pure state, dual to a black hole formed by gravitational collapse. The entanglement entropy grows linearly in time. This linear growth is directly related to the growth of the black hole interior measured along “nice” spatial slices. These nice slices probe the spacelike direction in the interior, at a fixed special value of the interior time. In the case of a two-dimensional CFT, we match the bulk and boundary computations of the entanglement entropy. We briefly discuss the long time behavior of various correlators, computed via classical geodesics or surfaces, and point out that their exponential decay comes about for similar reasons. We also present the time evolution of the wavefunction in the tensor network description.
736 citations
TL;DR: In this paper, the authors study chaos and scrambling in unitary channels by considering their entanglement properties as states and propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling.
Abstract: We study chaos and scrambling in unitary channels by considering their entanglement properties as states. Using out-of-time-order correlation functions to diagnose chaos, we characterize the ability of a channel to process quantum information. We show that the generic decay of such correlators implies that any input subsystem must have near vanishing mutual information with almost all partitions of the output. Additionally, we propose the negativity of the tripartite information of the channel as a general diagnostic of scrambling. This measures the delocalization of information and is closely related to the decay of out-of-time-order correlators. We back up our results with numerics in two non-integrable models and analytic results in a perfect tensor network model of chaotic time evolution. These results show that the butterfly effect in quantum systems implies the information-theoretic definition of scrambling.
649 citations