The role of conformal symmetry in the Jackiw–Pi model

The Jackiw–Pi model in 2+1$2+1$ dimensions is a non-relativistic conformal field theory of charged particles with point-like self-interaction. For specific values of the interaction strengths the classical theory possesses vortex and multi-vortex solutions, which are all degenerate in energy. We compute the full set of first-order perturbative quantum corrections. Only the coupling constant g²$g^2$ requires renormalization; the fields and electric charge e are not renormalized. It is shown that in general the conformal symmetries are broken by an anomalous contribution to the conservation law, proportional to the β-function. However, the β  -function vanishes upon restricting the coupling constants to values g²=±e²$g^2=\pm e^2$, which includes the case in which vortex solutions exist. Therefore the existence of vortices also guarantees the preservation of the conformal symmetries.     

Can the superstring inspire the standard model?

We discuss general features of models in which the E₈ × E′₈ heterotic superstring is compactified on a specific Calabi-Yau manifold. The gauge group of rank-6 in four dimensions is supposed to be broken down at an intermediate scale m_I to the standard model group SU(3)_C × SU(2)_L × U(1)_Y, as a result of two neutral scalar fields acquiring large vacuum expectations (vev's) in one of many flat directions of the effective potential. We find that it is difficult to generate such an intermediate scale by radiative symmetry breaking, whilst such models have prima facie problems with baryon decay mediated by massive particles and with non-perturbative behaviour of the gauge couplings, unless m_I ≳ 10¹⁶ GeV. Rapid baryon decay mediated by light particles, large neutrino masses, other Δ L ≠ 0 processes and flavour-changing neutral currents are generic features of these models. We illustrate these observations with explicit calculations in a number of different models given by vev's in different flat directions.     

Can the nearly conformal sextet gauge model hide the Higgs impostor?

New results are reported from large scale lattice simulations of a frequently discussed strongly interacting gauge theory with a fermion flavor doublet in the two-index symmetric (sextet) representation of the SU(3) color gauge group. We find that the chiral condensate and the mass spectrum of the sextet model are consistent with chiral symmetry breaking in the limit of vanishing fermion mass. In contrast, sextet fermion mass deformations of spectral properties are not consistent with leading conformal scaling behavior near the critical surface of a conformal theory. A recent paper could not resolve the conformal fixed point of the gauge coupling from the slowly walking scenario of a very small nearly vanishing β-function (DeGrand et al. [3]). It is argued that overall consistency with our new results is resolved if the sextet model is close to the conformal window, staying outside with a very small non-vanishing β-function. The model would exhibit then the simplest composite Higgs mechanism leaving open the possibility of a light scalar state with quantum numbers of the Higgs impostor. It would emerge as the pseudo-Goldstone dilaton state from spontaneous symmetry breaking of scale invariance. We will argue that even without association with the dilaton, the scalar Higgs-like state can be light very close to the conformal window. A new Higgs project of sextet lattice simulations is outlined to resolve these important questions.     

Is chiral symmetry restored in the excited meson spectrum?

The large degeneracy observed in the excited meson spectrum by the Cristal Barrel Collaboration in the experimental data on proton–antiproton annihilation in flight into mesons in the range 1.9–2.4 GeV has been interpreted as a signal of chiral symmetry restoration. In this work we suggest that such degeneracy may be an indication of the confinement potential modification by color screening. The experimental data can be fairly well reproduced in a constituent quark model with a screened linear confinement potential without changing the dynamical quark mass. Observables that could discriminate our model from those which explicitly restore the chiral symmetry are proposed.     

Is space-time symmetry a suitable generalization of parity-time symmetry?

We discuss space-time symmetric Hamiltonian operators of the form H=H₀+igH^′$H=H_0+ig{H}^{\prime }$, where H₀$H_0$ is Hermitian and g$g$ real. H₀$H_0$ is invariant under the unitary operations of a point group G$G$ while H^′$H^{\prime }$ is invariant under transformation by elements of a subgroup G^′$G^{\prime }$ of G$G$. If G$G$ exhibits irreducible representations of dimension greater than unity, then it is possible that H$H$ has complex eigenvalues for sufficiently small nonzero values of g$g$. In the particular case that H$H$ is parity-time symmetric then it appears to exhibit real eigenvalues for all 0<g<g_c$0<g<g_c$, where g_c$g_c$ is the exceptional point closest to the origin. Point-group symmetry and perturbation theory enable one to predict whether H$H$ may exhibit real or complex eigenvalues for g>0$g>0$. We illustrate the main theoretical results and conclusions of this paper by means of two- and three-dimensional Hamiltonians exhibiting a variety of different point-group symmetries.     

How much can one break chiral symmetry in the linear sigma model?

We show that the hedgehog soliton solution describing the nucleon in theSU(3) ×SU(3) linear sigma model breaks down when the pion mass becomes too large.On leave of absence from the Laboratoire de Physique Théorique, Université de Nice, parc Valrose, F-06034 Nice Cedex, France     

Hidden conformal symmetry of rotating black holes in the five-dimensional Gödel universe

We have investigated the hidden conformal symmetry of generic non-extremal rotating black holes in the five-dimensional Gödel universe. In a range of parameters, the low-frequency massless scalar wave equation in the “near region” can be described by an SL(2, R) _L × SL(2, R) _R conformal symmetry. We further found that the microscopic entropy via Cardy formula matches the macroscopic Bekenstein-Hawking entropy and the absorption cross section for the massless scalar also agrees with the one for the two dimensional finite temperature conformal field theory (CFT). All these evidences support the conjecture that the generic non-extremal rotating black hole immersed in the Gödel universe can be dual to a two dimensional finite temperature CFT. In addition, we have reformulated the first laws of thermodynamics associated with the inner and outer horizons of the rotating Gödel-type black holes into the forms of conformal thermodynamics.     

Is the Zee model neutrino mass matrix ruled out?

A very economic model of generating small neutrino masses is the Zee model. This model has been studied extensively in the literature with most of the studies concentrated on the simplest version of the model, where all diagonal entries in the mass matrix are zero. SNO, and KamLAND data disfavor this simple version, but only when one also combines information from atmospheric and K2K data can one rule out this model with a high confidence level. We show that the simplest version of the Zee model is ruled out at level. The original Zee model, however, contains more than enough freedom to satisfy constraints from the data. We propose a new form of mass matrix by a naturalness consideration. This new form of the mass matrix is consistent with all experimental data. It predicts that , and increases and decreases with |V_e3|. For and to be in their allowed regions, |V_e3| is sizeable but can be set below the 90% C.L. upper bound.Received: 8 December 2003, Published online: 19 March 2004     

Does the standard model of low-temperature glass dynamics describe a real glass?

We present the first experimental single-molecule (SM) spectroscopy study of the local dynamics in molecular glasses (frozen toluene and deuterated toluene weakly doped with a substituted terrylene) at T=2-30 K. Surprisingly, the dynamics does not follow the standard model of low-temperature glasses. An extra contribution to the dynamics was detected causing drifts and irreproducible jumps of the SM spectra. The isotope effects in the SM linewidth distribution and the density of states (boson peak) show that the fast dynamics at T=2 K is due to excitations of tunneling nature, whereas at T>7 K it is related to vibrations; H/D atoms are directly involved in both types of excitations.     

Is the neutral Knoevenagel reaction initiated by the carbanion formation?

The title reactions were studied by means of the density functional theory calculations. A base promoted reaction (called here ‘B’) was traced in a model composed of benzaldehyde, malononitrile, and (H₂O)₁₁. A neutral model (‘N’) of Ph‐CHO, H₂C(CN)₂ and (H₂O)₁₂ was also examined in line with a reported clean reaction. It was found that the ion pair of HC(CN) and H₃O⁺ is generated at the first step for N. For B, there are five elementary processes, and for N, four ones were obtained. By RB3LY/6‐311 + G** SCRF = PCM//RB3LYP/6‐31(+)G* energy calculations, the rate determining steps for both B and N reactions are the second proton removal, TS5(B) and TS3(N), respectively. In both B and N, the neutral species Ph(HO)HC‐CH(CN)₂ is the key intermediate. Copyright © 2010 John Wiley & Sons, Ltd.     

Is the quantum Hall effect influenced by the gravitational field?

Most of the experiments on the quantum Hall effect (QHE) were made at approximately the same height above sea level. A future international comparison will determine whether the gravitational field g(x) influences the QHE. In the realm of (1+2)-dimensional phenomenological macroscopic electrodynamics, the Ohm-Hall law is metric independent ("topological"). This suggests that it does not couple to g(x). We corroborate this result by a microscopic calculation of the Hall conductance in the presence of a post-Newtonian gravitational field.     

A relation between the Barbero–Immirzi parameter and the standard model

It has been shown that Sakharov's induced, from the fields entering the standard model, Barbero–Immirzi parameter γ assumes, in the framework of Euclidean formalism, the UV cutoff-independent value, 1/9. The calculus uses the Schwinger's proper-time formalism, the Seeley–DeWitt heat-kernel expansion, and it is akin to the derivation of the ABJ chiral anomaly in space–time with torsion.