Regge couplings and intercepts from the planar dual bootstrap

Planar unitarization of dual models is examined in terms of renormalized diagrams. The shift of the Reggeon intercept 1 ? α(0) and the renormalized coupling $\text{g}{}^2\text{N}\text{16π}$ are both expected of order unity in a model with SU(N) Chan-Paton factors. In four space-time dimensions Regge behaviour makes the shift of the dual photon mass reminiscent of Schwinger's mechanism.     

Pomeron factorization in general dual models

We demonstrate that in each ghost-free dual model with one minor restriction, there exists a critical dimensionality of space-time in which the pomeron singularity becomes a factorizable Regge pole. In each model when this dimensionality is chosen, the pomeron emerges with twice the intercept and half the slope of the leading secondary (f) trajectory. We explicitly construct the pomeron propagator and the operator coupling the pomeron to the reggeon sector for the general dual model, including the lower-lying negative-G-parity pomeron in the Neveu-Schwarz model. Gauge identities and physical states in the pomeron sector are also investigated. In all of the dual models the pomeron form factors exhibit a generalized f dominance and modified Wu-Yang behavior.     

Extreme waves statistics for the Ablowitz-Ladik system

We examine statistics of waves for the problem of modulation instability development in the framework of discrete integrable Ablowitz-Ladik (AL) system. Modulation instability depends on one free parameter h that has the meaning of the coupling between the nodes on the lattice. For strong coupling h ? 1, the probability density functions (PDFs) for waves amplitudes coincide with that for the continuous classical nonlinear Schrödinger equation; the PDFs for both systems are very close to Rayleigh ones. When the coupling is weak h ～ 1, there appear highly localized waves with very large amplitudes, that drastically change the PDFs to significantly non-Rayleigh ones, with so-called “fat tails” when the probability of a large wave occurrence is by several orders of magnitude higher than that predicted by the linear theory. Evolution of amplitudes for such rogue waves with time is similar to that of the Peregrine solution for the classical nonlinear Schrödinger equation.     

Character expansion methods for matrix models of dually weighted graphs

We consider generalized one-matrix models in which external fields allow control over the coordination numbers on both the original and dual lattices. We rederive in a simple fashion a character expansion formula for these models originally due to Itzykson and Di Francesco, and then demonstrate how to take the largeN limit of this expansion. The relationship to the usual matrix model resolvent is elucidated. Our methods give as a by-product an extremely simple derivation of the Migdal integral equation describing the largeN limit of the Itzykson-Zuber formula. We illustrate and check our methods by analysing a number of models solvable by traditional means. We then proceed to solve a new model: a sum over planar graphys possessing even coordination numbers on both the original and the dual lattice. We conclude by formulating the equations for the case of arbitrary sets of even, self-dual coupling constants. This opens the way for studying the deep problems of phase transitions from random to flat lattices. January 1995     

Poisson-Lie T-duality and Bianchi type algebras

All Bianchi bialgebras have been obtained. By introducing a non-degenerate adjoint invariant inner product over these bialgebras the associated Drinfeld doubles have been constructed, then by calculating the coupling matrices for these bialgebras several σ-models with Poisson-Lie symmetry have been obtained. Two simple examples as prototypes of Poisson-Lie dual models have been given.     

Electric-magnetic duality in non-abelian gauge theories

The duality transformation of the vacuum expectation value of the operator which creates magnetic vortices (the 't Hooft loop operator in the Higgs phase), is performed in the radial gauge (x_uA_u^a(x) = 0). It is found that in the weak coupling region (small g) of a pure Yang-Mills theory the dual operator creates electric vortices whose strength is $\text{1}\text{g}$. The theory is self-dual in this region, and the effective coupling of the dual Lagrangian is $\text{1}\text{g}$. (It is self-dual also in the extreme strong coupling region.) Thus the above duality transformation reduces to electric-magnetic duality where the electric field in the 't Hooft loop operators transforms into a magnetic field in the dual operator. In a spontaneously broken gauge theory these results are valid only within the region where the vortices (or the monopoles) are concentrated, or in directions of the algebra space of unbroken symmetry, as self-duality holds only for this subset of fields. Noting that the 't Hooft loop operator project into the subspace of these field configurations we find that it is an electric-magnetic duality for the spontaneously broken theory as well. In the strong coupling region a strong coupling expansion in powers $\text{1}\text{g}$ is suggested.     

Surface and quasi-longitudinal acoustic waves in KTiOAsO4 single crystals

Surface and quasi-longitudinal acoustic wave properties have been investigated in potassium titanyl arsenate (KTiOAsO₄, KTA) single crystals for the first time. Surface acoustic wave (SAW) velocity, electromechanical coupling coefficient and power flow angle characteristics have been obtained in rotated Y-cut of KTA crystals. High SAW electromechanical coupling coefficient (0.4%) is found in Z-cut of KTA crystals. For high-frequency devices it is promising the resonators on quasi-longitudinal acoustic wave in X-cut of KTA crystals with sharp response in interdigital transducer conductance at resonance frequency.     

Infinite order radiative corrections and renormalization

By means of the Ward identity and the correlation expansion derived earlier, we calculate virtual radiative corrections to an infinite order. Partial factorization of the correlation effects, as in the simple exchange processes, makes infinite summation possible. Furthermore, because the Ward identity is satisfied order by order and because we are able to carry out the infinite order summation and obtain a closed form, renormalization turns out to be very simple and transparent. Here the calculations are performed for a scalar: ?²: φ model, but are easily generalized to other similar models. We also indicate why this rearrangement of the ordinary perturbation expansion is suitable for strong coupling theories, ordinary local field theories as well as dual models.     

Some aspects of a unified approach to gauge,dual and Gribov theories

We consider quantum chromodynamics (QCD) with N_c colours and N_f flavours. Large N expansions for this theory are discussed and their advantages are pointed out, especially in relation to the possibility of unifying gauge, dual and Gribov theories of strong interactions. We first recall how the 1/N_c expansion of 't Hooft can be related to a dual loop expansion with a fixed coupling constant. We point out the necessity for quarkless (purely gluonic) bound states to appear and their importance in maintaining confinement at higher orders in 1/N_c. We show how non-orientable dual loops are reinterpreted in QCD and how a paradox appears when N_f is such that asymptotic freedom is lost. Some recent results of Cornwall and Tiktopoulos are analyzed in leading order in 1/N_c. We then introduce a 1/N expansion at ? ≡ N_f/N_c fixed and show how it is related to the hadronic topological expansion (TE). This allows an unambiguous definition of reggeon field theory concepts such as the bare pomeron and diffractive dissociation in QDC. We are able to relate the parameter ? to the clustering of hadronic final states into resonances. Decreasing ? corresponds to increasing cluster over gap size. Renormalization of the dual coupling constant as a function of ? is discussed and an apparent paradox is resolved. We are also able to shed some new light on the problem of f extinction in the TE.Finally, we compare our approach to other schemes trying to relate different aspects of hadron physics.     

Propagation of transverse sound waves in glasses at very low temperatures

For both longitudinal and transverse polarizations the variation of the velocity of sound has been measured in borosilicate glass BK7. The experiment has been carried out in the temperature range between 0.28 and 4.2 K and at frequencies between 30 and 150 MHz. The coupling between low energy two-level systems and phonons is found to be similar for both acoustic polarizations. Using our results we also calculate the magnitude of the thermal conductivity without additional assumptions and find complete agreement with existing experimental data.     

Phase diagrams in nonlocal Polyakov-Nambu-Jona-Lasinio models constrained by lattice QCD results

Based on lattice QCD-adjusted SU(2)f nonlocal Polyakov-Nambu-Jona-Lasinio (PNJL) models, we investigate how the location of the critical endpoint in the QCD phase diagram depends on the strenght of the vector meson coupling, as well as the Polyakov-loop (PL) potential and the form factors of the covariant model. The latter are constrained by lattice QCD data for the quark propagator. The strength of the vector coupling is adjusted such as to reproduce the slope of the pseudocritical temperature for the chiral phase transition at low chemical potential extracted recently from lattice QCD simulations. Our study supports the existence of a critical endpoint in the QCD phase diagram albeit the constraint for the vector coupling shifts its location to lower temperatures and higher baryochemical potentials than in the case without it.     

Surface plasmon THz waves on gratings

Because of their long propagation length at a metal surface in the far infrared, surface plasmons make potentially feasible the design and realization of 2D integrated terahertz systems over a metallic substrate. The coupling of a terahertz beam to the surface plasmon wave is very efficiently achieved by diffraction gratings engraved at the metal surface. In this article, we present a review of some recent works we performed in view of characterizing this coupling phenomenon. The analysis of the experimental data supplied by terahertz time-domain spectroscopy allows us to point out the main parameters that govern this diffraction process and the propagation of a surface plasmon over a flat or corrugated metal surface. To cite this article: M. Nazarov et al., C. R. Physique 9 (2008).     

Driven transverse shear waves in a strongly coupled dusty plasma

The linear dispersion properties of transverse shear waves in a strongly coupled dusty plasma are experimentally studied in a DC discharge device by exciting them in a controlled manner with a variable frequency external source. The dusty plasma is maintained in the strongly coupled fluid regime with (1<Γ?Γc) where Γ is the Coulomb coupling parameter and Γc is the crystallization limit. A dispersion relation for the transverse waves is experimentally obtained over a frequency range of 0.1 Hz to 2 Hz and found to show good agreement with viscoelastic theoretical results.     

Kosterlitz-thouless transition and self-duality in three dimensions

A class of self-dual globally symmetric Z_N models in three dimensions is presented. The limit N → ∞ is a type of anisotropic U(1) model (XY model) dual to a gas of integer point charges, interacting via a logarithmic potential in three dimensions. The latter is, at low temperature, nothing but a sine-Gordon theory with an anisotropic, logarithmic propagator. It therefore has a low-temperature Kosterlitz-Thouless phase and KT phase transition to a massive phase.The relation of the U(1) model to the thermodynamics of a helical magnet along the ferromagnetic-helical phase boundary in zero applied field (or to the smectic A to amectic C phase boundary in a liquid crystal) is indicated.     

Chiral symmetry breaking in QCD; Mesons as spin waves

The strong chiral symmetry breaking in Wilson's lattice version of QCD is discussed and interpreted as a necessary manifestation of the triangle anomaly. At strong coupling the effective hamiltonian acting in the s-wave hadron sector is found to describe a generalized antiferromagnet which is analyzed with the $\text{1}\text{2}\text{S}\text{(= 1/N, N = N}{}_{\mathrm{<mtext>color</mtext>}}\text{)}$ expansion known in the theory of magnetism. Mesons emerge as spin waves: pseudoscalars as Nambu-Goldstone bosons, vectors as “dormant” Goldstone bosons. Current and dynamical quark masses are identified, such that m_P² ∫ m(cur), m_v≈2[m(cur) + m(fyn)], and a fit to the particle spectrum gives m(dyn) = 390 MeV, m_u,d(cur) = 5.4 MeV, m_s(cur) = 140 MeV, m_c(cur) = 1.07 GeV. Static baryons emerge with a mass m_B = N[m(dyn) + m(cur)] + a contribution which is argued to vanish in the continuum limit. Vector and axial vector currents are defined on the lattice and studied at strong coupling. The relations $\text{1 =}\text{3}\text{5}\text{g}{}_{\mathrm{<mtext>A</mtext>}}\text{γ}{}_{\mathrm{?}}\text{(f}{}_{\mathrm{\pi }}\text{/m}{}_{\mathrm{?}}\text{)(Z}{}_{\mathrm{\pi }}\text{/Z}{}_{\mathrm{?}}\text{)}{}^{\mathrm{<mtext>1</mtext><mtext>2</mtext>}}$, Z_π/Z_? = 3.0 are found to agree with experiment. The resolution of the U(1) problem at strong coupling is discussed.     

Filamentation instabilities associated with ordinary electromagnetic waves in collisional plasmas

It is shown that parametric coupling of an ordinary electromagnetic wave with purely damped convective cell modes as well as other collisional modes leads to purely growing perturbations in the direction perpendicular to the incoming radiation. The excitation of purely growing modes in a magnetized plasma is important because the resulting E × B drift can cause particle transport across the external magnetic field.     

Conductivity from charge or spin density waves

Below a Peierls transition the coupled electron phonon collective mode plays an important role in the conductivity of one-dimensional metal models such as have been recently postulated for various organic compounds. Within the jellium model, or in an incommensurate situation, the mode frequency goes to zero for q → 0 and is responsible for the infinite conductivity first proposed by Fröhlich. Impurities, lattice commensurability and three dimensional ordering introduce a gap into the mode spectrum. The low frequency conductivity and a large dielectric constant are predicted. Similar effects are predicted for a spin density wave.     

Solitary dynamo waves

Long dynamo waves are a characteristic feature of interface dynamo models with spatially localized α and Ω effects. The evolution of such waves is described by the modified Korteweg–de Vries equation. Solutions to this equation take the form of solitary waves, breathers, and snoidal and cnoidal waves, and represent nonlinear waves of magnetic activity that migrate towards the equator, as observed on the Sun. Averaging techniques extend the theory to longer times and relate the amplitude of these waves to the dynamo number.     

Dual models in four dimensions with internal symmetries

Internal symmetries are introduced in dual models by compactifying N of the spacetime dimensions. Within the context of field theory, we have proved that this proposal is compatible with everyday experience. Dual models obtained in this way are shown to be mathematically self-consistent. In the dual spinor model a four-dimensional formalism is obtained by compactifying six of the directions, implying the existence of an SU(4) symmetry.     

The CPN−1 model: A strong coupling lattice approach

We develop large N character-like expansion techniques for vector and vector-like models. These are used to compute the mass gaps and beta functions in the d = 2 CP^N?1 models. Surprisingly there is an intermediate region where neither strong coupling nor perturbation theory is applicable. This “unknown” region is a consequence of the non-commutativity of strong coupling and large N, an interesting mathematical effect not found in other models and due to an interesting physical phenomenon: superconfinement.