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We propose a new sampling strategy, called smart active sapling, for quality inspections outside the production line. Based on the principles of active learning a machine learning model decides which samples are sent to quality inspection. On the one hand, this minimizes the production of scrap parts due to earlier detection of quality violations. On the other hand, quality inspection costs are reduced for smooth operation.

We study the time evolution of 2-point functions and entanglement entropy in strongly anisotropic, inhomogeneous and time-dependent N=4 super Yang-Mills theory in the large N and large 't Hooft coupling limit using AdS/CFT. On the gravity side this amounts to calculating the length of geodesics and area of extremal surfaces in the dynamical background of two colliding gravitational shockwaves, which we do numerically. We discriminate between three classes of initial conditions corresponding to wide, intermediate and narrow shocks, and show that they exhibit different phenomenology with respect to the nonlocal observables that we determine. Our results permit to use (holographic) entanglement entropy as an order parameter to distinguish between the two phases of the cross-over from the transparency to the full-stopping scenario in dynamical Yang-Mills plasma formation, which is frequently used as a toy model for heavy ion collisions. The time evolution of entanglement entropy allows to discern four regimes: highly efficient initial growth of entanglement, linear growth, (post) collisional drama and late time (polynomial) fall off. Surprisingly, we found that 2-point functions can be sensitive to the geometry inside the black hole apparent horizon, while we did not find such cases for the entanglement entropy., Comment: 28 pp, 9 figs; v2: updated references, changed color bars in Figure 2 and Figure 6

We present an extended version of a recently proposed semi-holographic model for heavy-ion collisions, which includes self-consistent couplings between the Yang-Mills fields of the Color Glass Condensate framework and an infrared AdS/CFT sector, such as to guarantee the existence of a conserved energy-momentum tensor for the combined system that is local in space and time, which we also construct explicitly. Moreover, we include a coupling of the topological charge density in the glasma to the same of the holographic infrared CFT. The semi-holographic approach makes it possible to combine CGC initial conditions and weak-coupling glasma field equations with a simultaneous evolution of a strongly coupled infrared sector describing the soft gluons radiated by hard partons. As a first numerical test of the semi-holographic model we study the dynamics of fluctuating homogeneous color-spin-locked Yang-Mills fields when coupled to a homogeneous and isotropic energy-momentum tensor of the holographic IR-CFT, and we find rapid convergence of the iterative numerical procedure suggested earlier., Comment: 1+26 pages, 5 figures; v2: slightly expanded version as to appear in JHEP

We consider dynamical black hole formation from a collapsing fluid described by a symmetric and flat FRW metric. Using the Hamilton-Jacobi method the local Hawking temperature for the formed trapping/apparent horizon is calculated. The local Hawking temperature depends on the tunneling path, which we take to be along a null direction $(\Delta s=0)$. We find that the local Hawking temperature depends directly on the equation of state of the collapsing fluid. We argue that Hawking radiation by quantum tunnelling from future inner and future outer trapping horizons is possible. However, only radiation from a space-like dynamical horizon has a chance to be observed by an external observer. Some comparison to existing literature is made., Comment: 13 pages, 4 figures

We determine holographically 2-point correlators of gauge invariant operators with large conformal weights and entanglement entropy of strips for a time-dependent anisotropic 5-dimensional asymptotically anti-de Sitter spacetime. At the early stage of evolution where geodesics and extremal surfaces can extend beyond the apparent horizon all observables vary substantially from their thermal value, but thermalize rapidly. At late times we recover quasi-normal ringing of correlators and holographic entanglement entropy around their thermal values, as expected on general grounds. We check the behaviour of holographic entanglement entropy and correlators as function of the separation length of the strip and find agreement with the exact expressions derived in the small and large temperature limits., Comment: 15 pages + appendices; v2: added references

We study the dynamics of gravitationally collapsing massive shells in AdS spacetime, and show in detail how one can determine extremal surfaces traversing them. The results are used to solve the time evolution of the holographic entanglement entropy in strongly coupled dual conformal gauge theory, which is is seen to exhibit a regime of linear growth independent of the shape of the boundary entangling region and the equation of state of the shell. Our exact results are finally compared to those of two commonly used approximation schemes, the Vaidya metric and the quasistatic limit, whose respective regions of validity are quantitatively determined., Comment: 22 pages + Appendices, 4 figures

We consider the time evolution of two entropy-like quantities, the holographic entanglement entropy and causal holographic information, in a model of holographic thermalization dual to the gravitational collapse of a thin planar shell. Unlike earlier calculations valid in different limits, we perform a full treatment of the dynamics of the system, varying both the shell's equation of state and initial position. In all cases considered, we find that between an early period related to the acceleration of the shell and a late epoch of saturation towards the thermal limit, the entanglement entropy exhibits universal linear growth in time in accordance with the prediction of Liu and Suh. As intermediate steps of our analysis, we explicitly construct a coordinate system continuous at the location of an infinitely thin shell and derive matching conditions for geodesics and extremal surfaces traversing this region., Comment: 7 pages, 8 figures; v2: References added and typos corrected

We investigate the behaviour of various correlators in N=4 super Yang Mills theory, taking finite coupling corrections into account. In the thermal limit we investigate the flow of the quasinormal modes as a function of the 't Hooft coupling. Then by using a specific model of holographic thermalization we investigate the deviation of the spectral densities from their thermal limit in an out-of-equilibrium situation. The main focus lies on the thermalization pattern with which the various plasma constituents of different energies approach their final thermal distribution as the coupling constant decreases from the infinite coupling limit. All results point towards the weakening of the usual top down thermalization pattern., Comment: HIP-2013-17-TH, Conference: C13-07-18

We present an analytical solution of a massless scalar field collapsing in a three dimensional space-time with a negative cosmological constant, i.e. asymptotically AdS_3. The Einstein and scalar field equations are formulated using double null Poincare coordinates. Trapping horizons form when a critical parameter is p > 1. There are indications that the horizon radius r_AH scales like r_AH ~ (p-1)^(1/4) and the black hole mass as M ~ r_AH^2 ~ (p-1)^(1/2), i.e. with a critical mass exponent of 1/2.

We investigate the behavior of energy momentum tensor correlators in holographic $\mathcal{N}=4$ super Yang-Mills plasma, taking finite coupling corrections into account. In the thermal limit we determine the flow of quasinormal modes as a function of the 't Hooft coupling. Then we use a specific model of holographic thermalization to study the deviation of the spectral densities from their thermal limit in an out-of-equilibrium situation. The main focus lies on the thermalization pattern with which the plasma constituents approach their thermal distribution as the coupling constant decreases from the infinite coupling limit. All obtained results point towards the weakening of the usual top-down thermalization pattern., Comment: 18 pages, 7 figures, v3: major revision

We investigate the behavior of the retarded Green's function of a U(1) gauge field in holographic N=4 Super Yang-Mills plasma, taking the leading strong coupling corrections into account. First, we use the thermal limit of this quantity to determine the flow of the photon quasinormal mode spectrum away from the infinite 't Hooft coupling limit, and after this specialize to a specific model of holographic thermalization, in which we evaluate the corresponding spectral density. In the latter case, our primary interest lies in the pattern, with which the spectral density approaches its equilibrium form, and how this process depends on the value of the coupling as well as the photon virtuality. All of the results obtained point consistently towards the weakening of the usual top/down pattern of holographic thermalization, once the coupling is decreased from the \lambda=infinity limit., Comment: 22 pages, 6 figures

We construct an algorithm to determine all stationary axi-symmetric solutions of 3-dimensional Einstein gravity with a minimally coupled self-interacting scalar field. We holographically renormalize the theory and evaluate then the on-shell action as well as the stress tensor and scalar one-point functions. We study thermodynamics, derive two universal formulas for the entropy and prove that global AdS provides a lower bound for the mass of certain solitons. Several examples are given in detail, including the first instance of locally asymptotically flat hairy black holes and novel asymptotically AdS solutions with non-Brown-Henneaux behavior., Comment: 52 pp, 4 figures, v2: corrected and rearranged discussion in beginning of section 2.1, added paragraph on light-like/time-like case at end of section 2.2

We use the AdS/CFT conjecture to investigate the thermalization of large-N_c N=4 Super Yang-Mills plasma in the limit of large but finite 't Hooft coupling. On the gravity side, we supplement the type IIB supergravity action by the full set of O(\alpha'^3) operators, which enables us to derive O(\lambda^{-3/2}) corrections to the emission spectrum of prompt photons in one model of holographic thermalization. Decreasing the coupling strength from the \lambda=\infty limit, we observe a qualitative change in the way the photon spectral density approaches its thermal limit as a function of the photon energy. We interpret this behavior as a sign of the thermalization pattern of the plasma shifting from top/down towards bottom/up., Comment: 5 pages, 3 figures; v2: minor corrections, added references

We study the production of prompt photons in strongly coupled out-of-equilibrium Super Yang-Mills plasma using the AdS/CFT correspondence. Our goal is to determine the photon emission spectrum at different stages of a thermalization process, which is modeled via the gravitational collapse of a thin spherical shell in AdS$_5$ space. Particular emphasis is placed on the limit of large frequencies, which we are able to treat analytically., Comment: 5 pages, 4 figures, v3: Minor mistake corrected in the calculations, figures and discussion adapted accordingly

We determine the out-of-equilibrium production rate of dileptons at rest in strongly coupled N=4 Super Yang-Mills plasma using the AdS/CFT correspondence. Thermalization is achieved via the gravitational collapse of a thin shell of matter in AdS_5 space and the subsequent formation of a black hole, which we describe in a quasistatic approximation. Prior to thermalization, the dilepton spectral function is observed to oscillate as a function of frequency, but the amplitude of the oscillations decreases when thermal equilibrium is approached. At the same time, we follow the flow of the quasinormal spectrum of the corresponding U(1) vector field towards its equilibrium limit., Comment: 21 pages, 7 figures. v2: Version accepted for publication in JHEP; minor modifications, added references

In the presence of a quark chemical potential, a magnetic field induces an axial current in the direction of the magnetic field. We compute this current in the Sakai-Sugimoto model, a holographic model which, in a certain limit, is dual to large-N_c QCD. We also compute the analogous vector current, for which an axial chemical potential is formally introduced. This vector current can potentially be observed via charge separation in heavy-ion collisions. After implementing the correct axial anomaly in the Sakai-Sugimoto model we find an axial current in accordance with previous studies and a vanishing vector current, in apparent contrast to previous weak-coupling calculations., Comment: 8 pages, to appear in the proceedings of "New Frontiers in QCD 2010", Yukawa Institute for Theoretical Physics, Kyoto, Japan, Jan 18 - Mar 19, 2010

We inspect the mass spectrum of heavy-light mesons in deformed N=2 super Yang-Mills theory using the AdS/CFT correspondence. We demonstrate how some of the degeneracies of the supersymmetric meson spectrum can be removed upon breaking the supersymmetry, thus leading to the emergence of hyperfine structure. The explicit SUSY breaking scenarios we consider involve on one hand tilting one of the two fundamental D7 branes inside the internal R^6 space, and on the other hand applying an external magnetic field on the (untilted) branes. The latter scenario leads to the well-known Zeeman effect, which we inspect for both weak and strong magnetic fields., Comment: 5 pages, 1 figure

In the chiral magnetic effect an imbalance in the number of left- and right-handed quarks gives rise to an electromagnetic current parallel to the magnetic field produced in noncentral heavy-ion collisions. The chiral imbalance may be induced by topologically nontrivial gluon configurations via the QCD axial anomaly, while the resulting electromagnetic current itself is a consequence of the QED anomaly. In the Sakai-Sugimoto model, which in a certain limit is dual to large-N_c QCD, we discuss the proper implementation of the QED axial anomaly, the (ambiguous) definition of chiral currents, and the calculation of the chiral magnetic effect. We show that this model correctly contains the so-called consistent anomaly, but requires the introduction of a (holographic) finite counterterm to yield the correct covariant anomaly. Introducing net chirality through an axial chemical potential, we find a nonvanishing vector current only before including this counterterm. This seems to imply the absence of the chiral magnetic effect in this model. On the other hand, for a conventional quark chemical potential and large magnetic field, which is of interest in the physics of compact stars, we obtain a nontrivial result for the axial current that is in agreement with previous calculations and known exact results for QCD., Comment: 35 pages, 4 figures, v2: added comments about frequency-dependent conductivity at the end of section 4; references added; version to appear in JHEP

The Sakai-Sugimoto model provides a holographic description for chiral symmetry breaking. We use this model to investigate chirally broken phases in an external magnetic field at finite isospin and baryon chemical potentials. The equations of motion for the bulk gauge fields are solved analytically and the free energy is computed from the Yang-Mills and Chern-Simons contributions to the D8 brane action. In the case of a neutral pion condensate, a magnetic field is found to induce nonzero gradients of the Goldstone boson fields corresponding to meson supercurrents. A charged pion condensate, on the other hand, expels the magnetic field due to the Meissner effect. Upon comparing the Gibbs free energies of these two phases we find that the rotation of the chiral condensate into a charged pion condensate for finite isospin chemical potentials is partially undone by switching on a magnetic field, and we determine the critical magnetic field which removes the charged pion condensate in a first-order phase transition., Comment: 46 pages, 5 figures, v2: small modifications and added footnotes in discussion of axial current and number density (p19, p24); typos corrected; references added; version to appear in JHEP

We use the AdS/CFT correspondence to compute the energy spectrum of heavy-light mesons in a N=2 SU(N) super Yang-Mills theory with two massive hypermultiplets. In the heavy quark limit, similar to QCD, we find that the excitation energies are independent of the heavy quark mass. We also make some remarks about related AdS/CFT models of flavor with less supersymmetry., Comment: 29 pages, 9 figures; v2 section 5 rewritten to include discussion of long strings, other minor improvements, ref added