Journal of High Energy Physics

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.

The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-k<sub>t</sub>'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split-merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plain ``iterative cone'' algorithm, for which the anti-k_t algorithm provides a natural, fast, infrared and collinear safe replacement.

This paper consists of three separate articles on the number of fundamental dimensionful constants in physics. We started our debate in summer 1992 on the terrace of the famous CERN cafeteria. In the summer of 2001 we returned to the subject to find that our views still diverged and decided to explain our current positions. LBO develops the traditional approach with three constants, GV argues in favor of at most two (within superstring theory), while MJD advocates zero.

There have long been known ``exact" β functions for the gauge coupling in N = 1 supersymmetric gauge theories, the so-called Novikov-Shifman-Vainshtein-Zakharov (NSVZ) β functions. Shifman and Vainshtein further related these β functions to the exact 1-loop running of the gauge coupling in a ``wilsonian" action. All these results, however, remain somewhat mysterious. We attempt to clarify these issues by presenting new perspectives on the NSVZ β function. Our interpretation of the results is somewhat different than the one given by Shifman and Vainshtein, having nothing to do with the distinction between ``wilsonian" and ``1PI" effective actions. Throughout we work in the context of the Wilsonian Renormalization Group; namely, as the cutoff of the theory is changed from M to M′, we seek to determine the appropriate changes in the bare couplings needed in order to keep the low energy physics fixed. The entire analysis is therefore free of infrared subtleties. When the bare lagrangian given at the cutoff is manifestly holomorphic in the gauge coupling, we show that the required change in the holomorphic gauge coupling is exhausted at 1-loop to all orders of perturbation theory, and even non-perturbatively in some cases. On the other hand, when the bare lagrangian at the cutoff has canonically normalized kinetic terms, we find that the required change in the gauge coupling is given by the NSVZ β function. The higher order contributions in the NSVZ β function are due to anomalous jacobians under the rescaling of the fields done in passing from holomorphic to canonical normalization. We also give prescriptions for regularizing certainN = 1 theories with an ultraviolet cutoff M preserving manifest holomorphy, starting from finite N = 4 and N = 2 theories. It is then at least in principle possible to check the validity of the exact β function by higher order calculations in these theories.

We consider the problem of how fast a quantum system can scramble (thermalize) information, given that the interactions are between bounded clusters of degrees of freedom; pairwise interactions would be an example. Based on previous work, we conjecture:

1. The most rapid scramblers take a time logarithmic in the number of degrees of freedom.

2. Matrix quantum mechanics (systems whose degrees of freedom are n byn matrices) saturate the bound.

3. Black holes are the fastest scramblers in nature.

We find more self-tuning solutions by introducing a general form for lagrangian of a 3-index antisymmetric tensor field A_MNP in the RS II model. In particular, for the logarithmic lagrangian, ∝log (−H²), we obtained a closed form weak self-tuning solution.

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

We propose a dual non-perturbative description for maximally extended Schwarzschild Anti-de-Sitter spacetimes. The description involves two copies of the conformal field theory associated to the AdS spacetime and an initial entangled state. In this context we also discuss a version of the information loss paradox and its resolution.

We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe.

Applying the first law of thermodynamics to the apparent horizon of a Friedmann-Robertson-Walker universe and assuming the geometric entropy given by a quarter of the apparent horizon area, we derive the Friedmann equations describing the dynamics of the universe with any spatial curvature. Using entropy formulae for the static spherically symmetric black hole horizons in Gauss-Bonnet gravity and in more general Lovelock gravity, where the entropy is not proportional to the horizon area, we are also able to obtain the Friedmann equations in each gravity theory. We also discuss some physical implications of our results.

A linear stability analysis of twisted flux-tubes (strings) in an SU(2) semilocal theory — an Abelian-Higgs model with two charged scalar fields with a global SU(2) symmetry — is carried out. Here the twist refers to a relative phase between the two complex scalars (with linear dependence on, say, the z coordinate), and importantly it leads to a global current flowing along the the string. Such twisted strings bifurcate with the Abrikosov-Nielsen-Olesen (ANO) solution embedded in the semilocal theory. Our numerical investigations of the small fluctuation spectrum confirm previous results that twisted strings exhibit instabilities whose amplitudes grow exponentially in time. More precisely twisted strings with a single magnetic flux quantum admit a continuous family of unstable eigenmodes with harmonic z dependence, indexed by a wavenumber k∊[−k_m, k_m]. Carrying out a perturbative semi-analytic analysis of the bifurcation, it is found that the purely numerical results are very well reproduced. This way one obtains not only a good qualitative description of the twisted solutions themselves as well as of their instabilities, but also a quantitative description of the numerical results. Our semi-analytic results indicate that in close analogy to the known instability of the embedded ANO vortex a twisted string is also likely to expand in size caused by the spreading out of its magnetic flux.

We provide a dual gravity description of a supersymmetric heavy nucleus, following the idea of our previous paper arXiv/0809.3141. The supersymmetric nucleus consists of a merginal bound state of A baryons distributed over a ball in 3 dimensions. In the gauge/string duality, the baryon in N = 4 super Yang-Mills (SYM) theory corresponds to a D5-brane wrapping S⁵ of the AdS₅×ばつS⁵ spacetime, so the nucleus corresponds to a collection of A D5-branes. We take a large A and a near horizon limits of a back-reacted geometry generated by the wrapped A D5-branes, where we find a gap in the supergravity fluctuation spectrum. This spectrum is a gravity dual of giant resonances of heavy nuclei, in the supersymmetric toy example of QCD.

We study the stochastic motion of a relativistic trailing string in black hole AdS₅. The classical string solution develops a world-sheet horizon and we determine the associated Hawking radiation spectrum. The emitted radiation causes fluctuations on the string both above and below the world-sheet horizon. In contrast to standard black hole physics, the fluctuations below the horizon are causally connected with the boundary of AdS. We derive a bulk stochastic equation of motion for the dual string and use the AdS/CFT correspondence to determine the evolution of a fast heavy quark in the strongly coupled N = 4 plasma. We find that the kinetic mass of the quark decreases by ΔM = −(γλ)^1/2T/2 while the correlation time of world sheet fluctuations increases by γ^1/2.

We present a complete treatment of the diffusion processes for supersymmetric electroweak baryogenesis that characterizes transport dynamics ahead of the phase transition bubble wall within the symmetric phase. In particular, we generalize existing approaches to distinguish between chemical potentials of particles and their superpartners. This allows us to test the assumption of superequilibrium (equal chemical potentials for particles and sparticles) that has usually been made in earlier studies. We show that in the Minimal Supersymmetric Standard Model, superequilibrium is generically maintained — even in the absence of fast supergauge interactions — due to the presence of Yukawa interactions. We provide both analytic arguments as well as illustrative numerical examples. We also extend the latter to regions where analytical approximations are not available since down-type Yukawa couplings or supergauge interactions only incompletely equilibrate. We further comment on cases of broken superequilibrium wherein a heavy superpartner decouples from the electroweak plasma, causing a kinematic bottleneck in the chain of equilibrating reactions. Such situations may be relevant for baryogenesis within extensions of the MSSM. We also provide a compendium of inputs required to characterize the symmetric phase transport dynamics.

Starting from the semiclassical reduced-action approach to transplanckian scattering by Amati, Veneziano and one of us and from our previous quantum extension of that model, we investigate theS-matrix expression for inelastic processes by extending to this case the tunneling features previously found in the region of classical gravitational collapse. The resulting model exhibits some non-unitary S-matrix eigenvalues for impact parameters b < b_c, a critical value of the order of the gravitational radiusR = 2Gs^1/2, thus showing that some (inelastic) unitarity defect is generally present, and can be studied quantitatively. We find that S-matrix unitarity for b < b_c is restored only if the rapidity phase-space parameter y is allowed to take values larger than the effective coupling Gs/ħ itself. Some features of the resulting unitary model are discussed.

In this article we will overview several aspects of the string landscape, namely intersecting D-brane models and their statistics, possible model independent LHC signatures of intersecting brane models, flux compactification, moduli stabilization in type II compactifications, domain wall solutions and brane inflation.

The k_t and Cambridge/Aachen inclusive jet finding algorithms for hadron-hadron collisions can be seen as belonging to a broader class of sequential recombination jet algorithms, parametrised by the power of the energy scale in the distance measure. We examine some properties of a new member of this class, for which the power is negative. This ``anti-k<sub>t</sub>'' algorithm essentially behaves like an idealised cone algorithm, in that jets with only soft fragmentation are conical, active and passive areas are equal, the area anomalous dimensions are zero, the non-global logarithms are those of a rigid boundary and the Milan factor is universal. None of these properties hold for existing sequential recombination algorithms, nor for cone algorithms with split-merge steps, such as SISCone. They are however the identifying characteristics of the collinear unsafe plain ``iterative cone'' algorithm, for which the anti-k_t algorithm provides a natural, fast, infrared and collinear safe replacement.

In the context of string theory, axions appear to provide the most plausible solution of the strong CP problem. However, as has been known for a long time, in many string-based models, the axion coupling parameter F_a is several orders of magnitude higher than the standard cosmological bounds. We re-examine this problem in a variety of models, showing that F_a is close to the GUT scale or above in many models that have GUT-like phenomenology, as well as some that do not. On the other hand, in some models with Standard Model gauge fields supported on vanishing cycles, it is possible for F_a to be well below the GUT scale.

We compute the three point correlation functions for primordial scalar and tensor fluctuations in single field inflationary models. We obtain explicit expressions in the slow roll limit where the answer is given terms of the two usual slow roll parameters. In a particular limit the three point functions are determined completely by the tilt of the spectrum of the two point functions. We also make some remarks on the relation of this computation to dS/CFT and AdS/CFT. We emphasize that (A)dS/CFT can be viewed as a statement about the wavefunction of the universe.

This is an extended version of our short report [1], where a holographic interpretation of entanglement entropy in conformal field theories is proposed from AdS/CFT correspondence. In addition to a concise review of relevant recent progresses of entanglement entropy and details omitted in the earlier letter, this paper includes the following several new results: We give a more direct derivation of our claim which relates the entanglement entropy with the minimal area surfaces in the AdS₃/CFT₂ case as well as some further discussions on higher dimensional cases. Also the relation between the entanglement entropy and central charges in 4D conformal field theories is examined. We check that the logarithmic part of the 4D entanglement entropy computed in the CFT side agrees with the AdS₅ result at least under a specific condition. Finally we estimate the entanglement entropy of massive theories in generic dimensions by making use of our proposal.

With an aim towards understanding the time-dependence of entanglement entropy in generic quantum field theories, we propose a covariant generalization of the holographic entanglement entropy proposal of hep-th/0603001. Apart from providing several examples of possible covariant generalizations, we study a particular construction based on light-sheets, motivated in similar spirit to the covariant entropy bound underlying the holographic principle. In particular, we argue that the entanglement entropy associated with a specified region on the boundary in the context of the AdS/CFT correspondence is given by the area of a co-dimension two bulk surface with vanishing expansions of null geodesics. We demonstrate our construction with several examples to illustrate its reduction to the holographic entanglement entropy proposal in static spacetimes. We further show how this proposal may be used to understand the time evolution of entanglement entropy in a time varying QFT state dual to a collapsing black hole background. Finally, we use our proposal to argue that the Euclidean wormhole geometries with multiple boundaries should be regarded as states in a non-interacting but entangled set of QFTs, one associated to each boundary.

We extend earlier ideas about the appearance of noncommutative geometry in string theory with a nonzero B-field. We identify a limit in which the entire string dynamics is described by a minimally coupled (supersymmetric) gauge theory on a noncommutative space, and discuss the corrections away from this limit. Our analysis leads us to an equivalence between ordinary gauge fields and noncommutative gauge fields, which is realized by a change of variables that can be described explicitly. This change of variables is checked by comparing the ordinary Dirac-Born-Infeld theory with its noncommutative counterpart. We obtain a new perspective on noncommutative gauge theory on a torus, its T-duality, and Morita equivalence. We also discuss the D0/D4 system, the relation to M-theory in DLCQ, and a possible noncommutative version of the six-dimensional (2,0) theory.

We show that all IIB supergravity backgrounds which admit more than 28 Killing spinors are maximally supersymmetric. In particular, we find that for all N>28 backgrounds the supercovariant curvature vanishes, and that the quotients of maximally supersymmetric backgrounds either preserve all 32 or N<29 supersymmetries.

I show that with simple extensions of the shower algorithms in Monte Carlo programs, one can implement NLO corrections to the hardest emission that overcome the problems of negative weighted events found in previous implementations. Simple variants of the same method can be used for an improved treatment of matrix element corrections in Shower Monte Carlo programs.

We conjecture a general upper bound on the strength of gravity relative to gauge forces in quantum gravity. This implies, in particular, that in a four-dimensional theory with gravity and a U(1) gauge field with gauge coupling g, there is a new ultraviolet scale Λ = gM_Pl, invisible to the low-energy effective field theorist, which sets a cutoff on the validity of the effective theory. Moreover, there is some light charged particle with mass smaller than or equal to Λ. The bound is motivated by arguments involving holography and absence of remnants, the (in) stability of black holes as well as the non-existence of global symmetries in string theory. A sharp form of the conjecture is that there are always light ``elementary'' electric and magnetic objects with a mass/charge ratio smaller than the corresponding ratio for macroscopic extremal black holes, allowing extremal black holes to decay. This conjecture is supported by a number of non-trivial examples in string theory. It implies the necessary presence of new physics beneath the Planck scale, not far from the GUT scale, and explains why some apparently natural models of inflation resist an embedding in string theory.

We study information retrieval from evaporating black holes, assuming that the internal dynamics of a black hole is unitary and rapidly mixing, and assuming that the retriever has unlimited control over the emitted Hawking radiation. If the evaporation of the black hole has already proceeded past the ``half-way'' point, where half of the initial entropy has been radiated away, then additional quantum information deposited in the black hole is revealed in the Hawking radiation very rapidly. Information deposited prior to the half-way point remains concealed until the half-way point, and then emerges quickly. These conclusions hold because typical local quantum circuits are efficient encoders for quantum error-correcting codes that nearly achieve the capacity of the quantum erasure channel. Our estimate of a black hole's information retention time, based on speculative dynamical assumptions, is just barely compatible with the black hole complementarity hypothesis.