arXiv subjects

Ben Craps

Publications and source records attributed to Ben Craps.

At least 55 records · Page 3Linked to original sources

arXiv2014

Renormalization group, secular term resummation and AdS (in)stability

We revisit the issues of non-linear AdS stability, its relation to growing (secular) terms in naive perturbation theory around the AdS background, and the need and possible strategies for resumming such terms. To this end, we review a powerful and elegant resummation method, which is mathematically identical to the standard renormalization group treatment of ultraviolet divergences in perturbative quantum field theory. We apply this method to non-linear gravitational perturbation theory in the AdS background at first non-trivial order and display the detailed structure of the emerging renormalization flow equations. We prove, in particular, that a majority of secular terms (and the corresponding terms in the renormalization flow equations) that could be present on general grounds given the spectrum of frequencies of linear AdS perturbations, do not in fact arise.

gr-qc↗

arXiv2014

Gravitational collapse and thermalization in the hard wall model

We study a simple example of holographic thermalization in a confining field theory: the homogeneous injection of energy in the hard wall model. Working in an amplitude expansion, we find black brane formation for sufficiently fast energy injection and a scattering wave solution for sufficiently slow injection. We comment on our expectations for more sophisticated holographic QCD models.

hep-th↗

arXiv2013

Strings in compact cosmological spaces

We confront the problem of giving a fundamental definition to perturbative string theory in spacetimes with totally compact space (taken to be a torus for simplicity, though the nature of the problem is very general) and non-compact time. Due to backreaction induced by the presence of even a single string quantum, the usual formulation of perturbative string theory in a fixed classical background is infrared-divergent at all subleading orders in the string coupling, and needs to be amended. The problem can be seen as a closed string analogue of D0-brane recoil under an impact by closed strings (a situation displaying extremely similar infrared divergences). Inspired by the collective coordinate treatment of the D0-brane recoil, whereby the translational modes of the D0-brane are introduced as explicit dynamical variables in the path integral, we construct a similar formalism for the case of string-induced gravitational backreaction, in which the spatially uniform modes of the background fields on the compact space are quantized explicitly. The formalism can equally well be seen as an ultraviolet completion of a minisuperspace quantum cosmology with string degrees of freedom. We consider the amplitudes for the universe to have two cross-sections with specified spatial properties and string contents, and show (at the first non-trivial order) that they are finite within our formalism.

hep-th↗

arXiv2013

The spectral function in a strongly coupled, thermalising CFT

In relation to the fluctuation-dissipation theorem, we discuss a time-dependent notion of spectral function and effective temperature. Extending recent results from arXiv:1212.6066, we work out these quantities in a two-dimensional thermalising CFT dual to AdS3-Vaidya spacetime which interpolates between a black brane geometry at early times and a higher temperature black brane at late times. The computation is carried out in the gravitational holographic dual in the geodesic approximation and using a non-standard analytic continuation.

hep-th↗

arXiv2013

Chern-Simons diffusion rate in a holographic Yang-Mills theory

Using holography, we compute the Chern-Simons diffusion rate of 4d gauge theories constructed by wrapping D4-branes on a circle. In the model with antiperiodic boundary conditions for fermions, we find that it scales like $T^6$ in the high-temperature phase. With periodic fermions, this scaling persists at low temperatures. The scaling is reminiscent of 6d hydrodynamic behavior even at temperatures small compared to compactification scales of the M5-branes from which the D4-branes descend. We offer a holographic explanation of this behavior by adding a new entry to the known map between D4 and M5 hydrodynamics, and suggest a field theory explanation based on "deconstruction" or "fractionization".

hep-th↗

arXiv2012

Holographic thermalization of mutual and tripartite information in 2d CFTs

We discuss the concepts of mutual and tripartite information by referring to simple intuitive examples, and describe their use as probes of thermalization in holographic models. We then review our computation of these quantities in a simple time dependent model, in which energy injection in a strongly coupled field theory is modeled by a shell of null dust falling into 3d anti-de Sitter space. We complete those results with a discussion of the possible equilibrium phases of the tripartite information.

hep-th↗

arXiv2012

On the Quantum Resolution of Cosmological Singularities using AdS/CFT

The AdS/CFT correspondence allows us to map a dynamical cosmology to a dual quantum field theory living on the boundary of spacetime. Specifically, we study a five-dimensional model cosmology in type IIB supergravity, where the dual theory is an unstable deformation of $\N=4$ supersymmetric SU(N) gauge theory on $\Rbar\times S^3$. A one-loop computation shows that the coupling governing the instability is asymptotically free, so quantum corrections cannot turn the potential around. The big crunch singularity in the bulk occurs when a boundary scalar field runs to infinity, in finite time. Consistent quantum evolution requires that we impose boundary conditions at infinite scalar field, i.e. a self-adjoint extension of the system. We find that quantum spreading of the homogeneous mode of the boundary scalar leads to a natural UV cutoff in particle production as the wavefunction for the homogeneous mode bounces back from infinity. However a perturbative calculation indicates that despite this, the logarithmic running of the boundary coupling governing the instability generally leads to significant particle production across the bounce. This prevents the wave packet of the homogeneous boundary scalar to return close to its initial form. Translating back to the bulk theory, we conclude that a quantum transition from a big crunch to a big bang is an improbable outcome of cosmological evolution in this class of five-dimensional models.

hep-th↗

arXiv2011

Light-like Big Bang singularities in string and matrix theories

Important open questions in cosmology require a better understanding of the Big Bang singularity. In string and matrix theories, light-like analogues of cosmological singularities (singular plane wave backgrounds) turn out to be particularly tractable. We give a status report on the current understanding of such light-like Big Bang models, presenting both solved and open problems.

hep-th↗

arXiv2011

Holographic Thermalization

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.

hep-th↗

arXiv2011

Adiabaticity and emergence of classical space-time in time-dependent matrix theories

We discuss the low-curvature regime of time-dependent matrix theories proposed to describe non-perturbative quantum gravity in asymptotically plane-wave space-times. The emergence of near-classical space-time in this limit turns out to be closely linked to the adiabaticity of the matrix theory evolution. Supersymmetry restoration at low curvatures, which is crucial for the usual space-time interpretation of matrix theories, becomes an obvious feature of the adiabatic regime.

hep-th↗

arXiv2010

D-Brane Potentials from Multi-Trace Deformations in AdS/CFT

It is known that certain AdS boundary conditions allow smooth initial data to evolve into a big crunch. To study this type of cosmological singularity, one can use the dual quantum field theory, where the non-standard boundary conditions are reflected by the presence of a multi-trace potential unbounded below. For specific AdS_4 and AdS_5 models, we provide a D-brane (or M-brane) interpretation of the unbounded potential. Using probe brane computations, we show that the AdS boundary conditions of interest cause spherical branes to be pushed to the boundary of AdS in finite time, and that the corresponding potential agrees with the multi-trace deformation of the dual field theory. Systems with expanding spherical D3-branes are related to big crunch supergravity solutions by a phenomenon similar to geometric transition.

hep-th↗

arXiv2010

The cosmological singularity problem

Despite impressive phenomenological successes, cosmological models are incomplete without an understanding of what happened at the big bang singularity. Depending on the model, one would like to understand how appropriate initial conditions were selected at the big bang singularity, or how a pre-existing contracting universe underwent a big crunch/big bang transition, if such transitions are possible at all. In this talk, after an introduction to these questions, an attempt is described to study cosmological singularities using the AdS/CFT correspondence. A specific model in which asymptotically AdS initial data evolve into a big crunch singularity is discussed and a dual field theory description is provided.

hep-th↗

arXiv2009

p-branes on the waves

We present a large family of simple, explicit ten-dimensional supergravity solutions describing extended extremal supersymmetric Ramond-Ramond p-branes embedded into time-dependent dilaton-gravity plane waves of an arbitrary (isotropic) profile, with the brane world-volume aligned parallel to the propagation direction of the wave. Generalizations to the non-extremal case are not analyzed explicitly, but can be pursued as indicated.

hep-th↗

arXiv2009

A multitrace deformation of ABJM theory

Motivated by the study of big crunch singularities in asymptotically $AdS_4$ spacetimes, we consider a marginal triple trace deformation of ABJM theory. The deformation corresponds to adding a potential which is unbounded below. In a 't Hooft large N limit, the beta function for the triple trace deformation vanishes, which is consistent with the near-boundary behavior of the bulk fields. At the next order in the 1/N expansion, the triple trace couplings exhibit non-trivial running, which we analyze explicitly in the limit of zero 't Hooft coupling, in which the model reduces to an $O(N)\times O(N)$ vector model with large N. In this limit, we establish the existence of a perturbative UV fixed point, and we comment on possible non-perturbative effects. We also show that the bulk analysis leading to big crunch singularities extends to the $\Zbar_k$ orbifold models dual to ABJM theory.

hep-th↗

arXiv2009

Can free strings propagate across plane wave singularities?

We study free string propagation in families of plane wave geometries developing strong scale-invariant singularities in certain limits. We relate the singular limit of the evolution for all excited string modes to that of the center-of-mass motion (the latter existing for discrete values of the overall plane wave profile normalization). Requiring that the entire excitation energy of the string should be finite turns out to be quite restrictive and essentially excludes consistent propagation across the singularity, unless dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).

hep-th↗

arXiv2009

Free string evolution across plane wave singularities

In these proceedings, we summarize our studies of free string propagation in (near-)singular scale-invariant plane wave geometries. We analyze the singular limit of the evolution for the center-of-mass motion and all excited string modes. The requirement that the entire excitation energy of the string should be finite excludes consistent propagation across the singularity, in case no dimensionful scales are introduced at the singular locus (in an otherwise scale-invariant space-time).

hep-th↗

arXiv2008

Quantum evolution across singularities: the case of geometrical resolutions

We continue the study of time-dependent Hamiltonians with an isolated singularity in their time dependence, describing propagation on singular space-times. In previous work, two of us have proposed a "minimal subtraction" prescription for the simplest class of such systems, involving Hamiltonians with only one singular term. On the other hand, Hamiltonians corresponding to geometrical resolutions of space-time tend to involve multiple operator structures (multiple types of dependence on the canonical variables) in an essential way. We consider some of the general properties of such (near-)singular Hamiltonian systems, and further specialize to the case of a free scalar field on a two-parameter generalization of the null-brane space-time. We find that the singular limit of free scalar field evolution exists for a discrete subset of the possible values of the two parameters. The coordinates we introduce reveal a peculiar reflection property of scalar field propagation on the generalized (as well as the original) null-brane. We further present a simple family of pp-wave geometries whose singular limit is a light-like hyperplane (discontinuously) reflecting the positions of particles as they pass through it.

hep-th↗

arXiv2008

Quantum evolution across singularities

Attempts to consider evolution across space-time singularities often lead to quantum systems with time-dependent Hamiltonians developing an isolated singularity as a function of time. Examples include matrix theory in certain singular time-dependent backgounds and free quantum fields on the two-dimensional compactified Milne universe. Due to the presence of the singularities in the time dependence, the conventional quantum-mechanical evolution is not well-defined for such systems. We propose a natural way, mathematically analogous to renormalization in conventional quantum field theory, to construct unitary quantum evolution across the singularity. We carry out this procedure explicitly for free fields on the compactified Milne universe and compare our results with the matching conditions considered in earlier work (which were based on the covering Minkowski space).

hep-th↗