Narrow Results

We employed high-density microelectrode arrays to investigate spontaneous firing patterns of neurons in brain circuits of the primary somatosensory cortex (S1) in mice. We recorded from over 150 neurons for 10min in each of eight different experiments, identified their location in S1, sorted their action potentials (spikes), and computed their power spectra and inter-spike interval (ISI) statistics. Of all persistently active neurons, 92% fired with a single dominant frequency — regularly firing neurons (RNs) — from 1 to 8Hz while 8% fired in burst with two dominant frequencies — bursting neurons (BNs) — corresponding to the inter-burst (2–6Hz) and intra-burst intervals (20–160Hz). RNs were predominantly located in layers 2/3 and 5/6 while BNs localized to layers 4 and 5. Across neurons, the standard deviation of ISI was a power law of its mean, a property known as fluctuation scaling, with a power law exponent of 1 for RNs and 1.25 for BNs. The power law implies that firing and bursting patterns are scale invariant: the firing pattern of a given RN or BN resembles that of another RN or BN, respectively, after a time contraction or dilation. An explanation for this scale invariance is discussed in the context of previous computational studies as well as its potential role in information processing.

In January 1999, the authors published a quantitative prediction that the Nikkei index should recover from its 14-year low in January 1999 and reach ≈20 500 a year later. The purpose of the present paper is to evaluate the performance of this specific prediction as well as the underlying model: the forecast, performed at a time when the Nikkei was at its lowest (as we can now judge in hindsight), has correctly captured the change of trend as well as the quantitative evolution of the Nikkei index since its inception. As the change of trend from sluggish to recovery was estimated quite unlikely by many observers at that time, a Bayesian analysis shows that a skeptical (resp. neutral) Bayesian sees prior belief in our model amplified into a posterior belief 19 times larger (resp. reach the 95% level).

We propose that the herding behavior of traders leads not only to speculative bubbles with accelerating over-valuations of financial markets possibly followed by crashes, but also to "anti-bubbles" with decelerating market devaluations following all-time highs. For this, we propose a simple market dynamics model in which the demand decreases slowly with barriers that progressively quench in, leading to a power law decay of the market price characterized by decelerating log-periodic oscillations. We document this behavior of the Japanese Nikkei stock index from 1990 to present and of the gold future prices after 1980, both after their all-time highs. We perform simultaneously parametric and nonparametric analyses that are fully consistent with each other. We extend the parametric approach to the next order of perturbation, comparing the log-periodic fits with one, two and three log-frequencies, the latter providing a prediction for the general trend in the coming years. The nonparametric power spectrum analysis shows the existence of log-periodicity with high statistical significance, with a preferred scale ratio of λ≈3.5 for the Nikkei index and λ≈1.9 for the Gold future prices, comparable to the values obtained for speculative bubbles leading to crashes.

The energy density of the universe today may be dominated by the vacuum energy of a slowly rolling scalar field. Making a quantum expansion around such a time-dependent solution breaks fundamental symmetries of quantum field theory. We call this mechanism cosmological symmetry breaking and argue that it is different from the standard phenomenon of spontaneous symmetry breaking. We illustrate this with a toy scalar field theory, whose action displays a U(1) symmetry. We identify a symmetry, called pseudo-scale invariance, which sets the cosmological constant exactly equal to zero, both in classical and quantum theories. This symmetry is also broken cosmologically and leads to a nonzero vacuum or dark energy. The slow-roll condition along with the observed value of dark energy leads to a value of the background scalar field of the order of Planck mass. We also consider a U(1) gauge symmetry model. Cosmological symmetry breaking, in this case, leads to a nonzero mass for the vector field. We also show that a cosmologically broken pseudo-scale invariance can generate a wide range of masses.

We consider a generalization of Einstein's general theory of relativity such that it respects local scale invariance. This requires the introduction of a scalar and a vector field in the action. We show that the theory naturally displays both dark energy and dark matter. We solve the resulting equations of motion assuming an FRW metric. The solutions are found to be almost identical to those corresponding to the standard ΛCDM model.

We consider the standard model with local scale invariance. The theory shows exact scale invariance of dimensionally regulated action. We show that massless gauge fields, which may be Abelian or non-Abelian, lead to vanishing contribution to the cosmological constant in this theory. This result follows in the quantum theory, to all orders in the gauge couplings. However, we have not considered contributions higher orders in the gravitational coupling. Similarly we also find that massless fermion fields yield null contribution to the cosmological constant. The effective cosmological constant in this theory is nonzero due to the phenomenon of cosmological symmetry breaking, which also gives masses to all the massive fields, besides generating the Planck mass. We find a simple relationship between the curvature scalar and the vacuum value of the Higgs field in the limit when we ignore all other contributions to the energy density besides the vacuum energy.

We construct a gravity dual for scale invariant but non-conformal field theories with a cyclic renormalization group flow. A slight modification of our construction gives a gravity dual of discretely scale invariant field theories. The underlying gravitational theory breaks the null energy condition.

The derivation of the a-theorem recently proposed by Komargodski and Schwimmer relies on the ϵ-conjecture that demands decoupling of dilaton from the rest of the infrared theory. We point out that the decoupling, if true, provides a strong evidence for the equivalence between scale invariance and conformal invariance in four dimensions. Thus, a complete proof of the a-theorem along the line of their argument in the most generic scenario would establish the equivalence between scale invariance and conformal invariance, which is another long-standing conjecture in four-dimensional quantum field theories.

We study a model with global scale invariance within the framework of unimodular gravity. The global scale invariant gravitational action which follows the unimodular general coordinate transformations is considered without invoking any scalar field. This is generalization of conformal theory described [P. D. Mannheim and D. Kazanas, Astrophys. J.342, 635 (1989)]. The possible solutions for the gravitational potential under static linear field approximation are discussed. The new modified solution has additional corrections to the Schwarzschild solution which describe the galactic rotational curve. A comparative study of unimodular theory with conformal theory is also presented. Furthermore, the cosmological solution is studied and it is shown that the unimodular constraint preserve the de Sitter solution explaining the dark energy of the universe.

We propose a model of a confining dark sector, dark technicolor, that communicates with the Standard Model (SM) through the Higgs portal. In this model electroweak (EW) symmetry breaking and dark matter (DM) share a common origin, and the EW scale is generated dynamically. Our motivation to suggest this model is the absence of evidence for new physics from recent Large Hadron Collider (LHC) data. Although the conclusion is far from certain at this point, this lack of evidence may suggest that no mechanism exists at the EW scale to stabilize the Higgs mass against radiative corrections from ultraviolet (UV) physics. The usual reaction to this puzzling situation is to conclude that the stabilizing new physics is either hidden from us by accident, or that it appears at energies that are currently inaccessible, such that nature is indeed fine-tuned. In order to re-examine the arguments that have led to this dichotomy, we review the concept of naturalness in effective field theories, discussing in particular the role of quadratic divergences in relation to different energy scales. This leads us to suggest classical scale invariance as a guideline for model building, implying that explicit mass scales are absent in the underlying theory.

Starting with a simple two-scalar field system coupled to a modified measure that is independent of the metric, we, first, find a Born–Infeld dynamics sector of the theory for a scalar field and second, show that the initial scale invariance of the action is dynamically broken and leads to a scale charge nonconservation, although there is still a conserved dilatation current.

We consider the relation between scale invariance and conformal invariance. In our analysis the variation of the metric is taken into account. By imposing some conditions on the trace of the energy–momentum tensor and on the variation of the action, we find that the scale dimensions of the fields are not affected. We also obtain the conserved currents. We find that the conditions for conformal invariance are stronger than for scale invariance.

The concept of exact and broken scale invariance is discussed. We give a brief introduction to unparticle physics. The neutral meson mixing can be caused by exchange of unparticle at the tree level. The constraints on interaction between unparticle and SM quarks are discussed.

Phenomenology of unparticle physics at linear as well as hadron colliders was briefly reviewed in this talk, including real emissions and virtual exchanges of unparticle. Existing constraints from collider as well as astrophysics experiments were briefly discussed.

The relation between scale invariance and conformal invariance is a subtle but important unsolved problem in the quantum field theory. We study a holographic approach to this problem and show that the null energy condition in the bulk effective gravitational theories guarantees the equivalence between the scale invariance and conformal invariance of the boundary theories. We also investigate the higher-dimensional compactification, where the warping can generate additional possible violation of the conformal invariance. Our discussion is applicable in any dimension, and suggests a generalization of Zamolodchikov–Polchinski theorem that states the equivalence in (1+1) dimension from the purely field theory viewpoint.

In contrast to the folklore that Technicolor (TC) is a "Higgsless theory", we shall discuss existence of a composite Higgs boson, Techni-Dilaton (TD), a pseudo-Nambu-Goldstone boson of the scale invariance in the Scale-invariant/Walking/Conformal TC (SWC TC) which generates a large anomalous dimension γ_m ≃ 1 in a wide region from the dynamical mass of the techni-fermion all the way up to the intrinsic scale Λ_TC of the SWC TC (analogue of Λ_QCD), where Λ_TC is taken typically as the scale of the Extended TC scale Λ_ETC: Λ_TC ≃ Λ_ETC ~ 10³TeV (≫ m). All the techni-hadrons have mass on the same order , which in SWC TC is extremely smaller than the intrinsic scale Λ_TC ≃ Λ_ETC, in sharp contrast to QCD where both are of the same order. The mass of TD arises from the non-perturbative scale anomaly associated with the techni-fermion mass generation and is typically 500-600 GeV, even smaller than other techni-hadrons of the same order of , in another contrast to QCD which is believed to have no scalar bound state lighter than other hadrons. We discuss the TD mass in various methods, Gauged NJL model via ladder Schwinger-Dyson (SD) equation, straightforward calculations in the ladder SD/ Bethe-Salpeter equation, and the holographic approach including techni-gluon condensate. The TD may be discovered in LHC.

We investigate a possibility of scale invariant but nonconformal supersymmetric field theories from a perturbative approach. The explicit existence of monotonically decreasing a-function that generates beta-functions as a gradient flow provides a strong obstruction for such a possibility at two-loop order. We comment on the "discovery" of scale invariant but nonconformal renormalization group trajectories via a "change of scheme" in (4-ϵ) dimension proposed in literatures.

We study the interaction between two B = 1 states in the Chiral Dilaton Model where baryons are described as nontopological solitons arising from the interaction of chiral mesons and quarks. By using the hedgehog solution for B = 1 states we construct, via a product ansatz, three possible B = 2 configurations to analyse the role of the relative orientation of the hedgehog quills in the dynamics of the soliton–soliton interaction and investigate the behavior of these solutions in the range of long/intermediate distance. One of the solutions is quite binding due to the dynamics of the π and σ fields at intermediate distance and should be used for nuclear matter studies. Since the product ansatz break down as the two solitons get close, we explore the short range distance regime with a model that describes the interaction via a six-quark bag ansatz. We calculate the interaction energy as a function of the inter-soliton distance and show that for small separations the six quarks bag, assuming a hedgehog structure, provides a stable bound state that at large separations connects with a special configuration coming from the product ansatz.

We consider scale invariant models where the classical scale invariance is broken perturbatively by radiative corrections at the electroweak scale. These models potentially offer an elegant and simple solution to the hierarchy problem. If we further require the cosmological constant to be small then such models are also highly predictive. Indeed, the minimal such model, comprizing a Higgs doublet and a real singlet, has the same number of parameters as the standard model. Although this minimal model is disfavored by recent LHC data, we show that two specific extensions incorporating neutrino masses and dark matter are fully realistic. That is, consistent with all experiments and observations. These models predict a light pseudo-Goldstone boson, h, with mass around 10 GeV or less. A fermionic-bosonic mass relation is also predicted. The specific models considered, as well as more generic scale invariant models, can be probed at the LHC.

These are intended to be review notes on emergent symmetries, i.e. symmetries which manifest themselves in specific sectors of energy in many systems. The emphasis is on the physical aspects rather than computation methods. We include some background material and go through more recent problems in field theory, statistical mechanics and condensed matter. These problems illustrate how some important symmetries, such as Lorentz invariance and supersymmetry, usually believed to be fundamental, can arise naturally in low-energy regimes of systems involving a large number of degrees of freedom. The aim is to discuss how these examples could help us to face other complex and fundamental problems.