Hybrid mesons and instantons

The scalar quark—gluon current for describing hybrids with quantum numbersJ ^PC=0 ⁺⁺ is studied by the method of QCD sum rules. The contribution of direct instantons to the correlation function of this current instantonfluid model is calculated. It is shown that in the mass rangeM _R5 GeV the QCD sum rule in this channel admits the existence of resonance structure, which at lower masses is destroyed by instanton interactions.Translated from Izvestiya Vysshykh Uchebnykh Zavedenii, Fizika, No. 8, pp. 95–102, August, 1993.     

Heavy quarkonia properties at high temperatures

The spectra and e ⁺ e ⁻ decay widths of the heavy quarkonia as a function of the temperature of medium generated in the ultrarelativistic heavy-ion collisions are discussed. The fluctuations of the vacuum gluon fields are estimated within the instanton liquid model approach. It is noticed that the parameters that are considered can be used to indicate the gluon warming.     

Large orders in the 1/N perturbation theory by inverse scattering in one dimension

When one tries to compute large orders in the 1/N series à la Lipatov a complicated non-linear equation for the instanton is found in ø⁴ or non-linear sigma models.We solve here this equation in the one-dimensional case (quantum mechanics) by inverse scattering techniques. From the instanton solutions we obtain theK ^th order of the 1/N perturbation theory up to 0(K ^–1) for the 0(N) symmetric anharmonic oscillator and up to a factor 0(K ⁰) for a non-symmetric model. In the symmetric case we agree with results recently obtained in quantum mechanics by Hikami and Brézin following a different procedure. For the non-symmetric anharmonic oscillator we believe our formulae are new.     

Instantons and Asymmetric Vacua

It is shown that with asymmetric classical vacua the quantum mechanical instanton approach to the energy splitting of degenerate states applies even though the degenerate state in one well is not the quantum mechanical ground state of that well. The instanton approach leads to the correct leading exponential behavior of the energy splitting E, but the prefactor is much more difficult to compute due to the asymmetric nature of the fluctuation potential V(_c(t)), which is in turn a direct consequence of the asymmetry of the two classical minima between which the instanton interpolates.     

The many vacua of gauged extended supergravities

A novel method is presented which employs advanced numerical techniques used in the engineering sciences to find and study the properties of nontrivial vacua of gauged extended supergravity models. While this method only produces approximate numerical data rather than analytic results, it overcomes the previous limitation of only being able to find vacua with large residual unbroken gauge symmetry groups. The effectiveness of this method is demonstrated by applying it to the technically most challenging D ≥ 3 scalar potential—that of SO(8) × SO(8) gauged Chern–Simons Supergravity in D = 3. Extensive data on the properties of 99 different vacua (92 of them new) of this model are given. Furthermore, techniques are briefly discussed which should allow using this numerical information as an input to the construction of semi-automatic stringent analytic proofs on the locations and properties of vacua. It hence is argued that these combined techniques presumably are powerful enough to systematically map all the nontrivial vacua of every supergravity model.     

Spectrum of heavy quarkonia in an instanton medium

The energy-level shift in heavy-quarkonium systems that is caused by fluctuations of vacuum gluon fields is estimated by simulating these fields by an instanton liquid. The use of the corresponding vacuum correlation function makes it possible to go beyond the dipole approximation. The width of energy levels with respect to decay to e ⁺ e ^? pairs is also given. It is shown that, both for bottomonium and for charmonium systems, an instanton medium can ensure a scale of shifts and widths of levels that is compatible with experimental data. In particular, it is indicated that a sizable logarithmic contribution at short distances is peculiar to the instanton vacuum.     

The classical nucleation rate in two dimensions

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. In homogeneous nucleation theory the nucleation rate can be written in the form of the Arrhenius law: . Here is the energy of the critical bubble, and the prefactor can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. In general it is not possible to find explicit expressions for and . If the difference between the energies of the stable and metastable vacua is small, the constant can be determined within the leading approximation in , which is an extension of the ”thin wall approximation”. We have done this calculation for the case of a model with a real-valued order parameter in two dimensions. Received: 11 September 2002 / Revised version: 30 October 2002 / Published online: 24 January 2003 RID="a" ID="a" e-mail: munsteg@uni-muenster.de RID="b" ID="b" e-mail: rut@ifttp.bas-net.by ^* Present address: Universit?t Essen, Fachbereich 7 - Physik, Universit?tsstr. 5, 45117 Essen, Germany     

Large-n limit of the Heisenberg model: The decorated lattice and the disordered chain

The critical temperature of the generalized spherical model (large-component limit of the classical Heisenberg model) on a cubic lattice, whose every bond is decorated byL spins, is found. WhenL, the asymptotics of the temperature isT _c aL ^–1. The reduction of the number of spherical constraints for the model is found to be fairly large. The free energy of the one-dimensional generalized spherical model with random nearest neighbor interaction is calculated.     

Long-Range Orders in Models of Itinerant Electrons Interacting with Heavy Quantum Fields

The Falicov–Kimball model consists of itinerant lattice fermions interacting with Ising spins by an on-site potential of strength U. Kennedy and Lieb proved that at half filling there is a low temperature phase with chessboard long range order on ^d , d2, for all non-zero values of U. Here we investigate the stability of this phase when small quantum fluctuations of the Ising spins are introduced in two different ways. The first one corresponds to replace the classical spins by quantum two level systems attached to each site of the lattice. In the second one we interpret the spins as occupation numbers of localized f-electrons or heavy ions which have a small kinetic energy. This leads to the so-called asymmetric Hubbard model. For both models we prove that for all non-zero values of U the long range order of the original Falicov–Kimball model remains stable if the additional quantum fluctuations are small enough. This result is proved by non-perturbative methods based on a chessboard estimate and the principle of exponential localisation. In order to derive the chessboard estimate the phase factors in the kinetic energy of fermions must have a flux equal to . We also investigate the models where the fermions are replaced by hard-core bosons and prove the same result for large U. For hard core bosons the kinetic term is the conventional one with zero phase factors. For small U and hard-core bosons we find that there is an off-diagonal long range order for low enough temperature and any strength of the additional quantum fluctuations. Open problems are discussed.     

Thermodynamics of chromomagnetism

The thermodynamics of a system of gluons interacting with a constant color magnetic field is investigated. There is a first-order phase transition from a magnetic state at low temperature to a non-magnetic state at high temperature. The transition temperature corresponds closely to the critical temperatures obtained in a perturbative expansion, in the finite temperature dilute instanton gas approximation, and in the MIT bag model. The free energy of a heavy quark-antiquark pair increases linearly with distance below the transition temperature but decreases coulombically above it.     

Phase transitions between axisymmetric and nonaxial nuclear shapes

Within the interacting-boson model, phase transitions between different nuclear shapes are considered in the space of three control parameters. Depending on the values of these parameters, the equilibrium shape of a nucleus can be spherical, axially deformed, or nonaxial. It is shown that the phase transition from an axisymmetric to a nonaxial deformation is a second-order phase transition. Within the Bohr-Mottelson model, an approximate solution is found that describes a nucleus in the vicinity of the critical point of a phase transition from a spherical to nonaxially deformed shape. The results obtained for the energies and E2-transition probabilities are close to experimental data for the ¹³⁴Ba nucleus.     

TheCP N−1 1/N-action by inverse scattering transformation in angular momentum

The effective action which generates 1/N expansion of theCP _N–1 model in two dimensions is studied here by inverse-problem methods. The action contains a functional determinant, in which auxiliary scalar and vector fields are assumed to have a spherical symmetry. This leads to the introduction, as an associated linear problem, of a radial Schrödinger equation with two potentialsv and , and a potential-dependent centrifugal term {(–r)²/r ²–1/4r ²}. The full inverse scattering formalism is developed here for this diffusion problem. It is formulated in terms of two-component Jost solutions, and leads to a matricial Gel'fand-Levitan-Marchenko equation. The scattering data associated to the potentials by this IST are then used to obtain a closed local form for the whole effective action. This is indeed possible for theCP _N–1 model, owing to the classical integrability. Moreover it is found that no spherically symmetric instanton exists in this case. However the absence of supplementary informations on the 1/N series, due to the non-integrability at quantum level, does not allow safe quantitative conclusions on the general behaviour of the 1/N series at large orders.Laboratoire associé au CNRS UA 280     

Finite-size shift of the critical temperature in the spherical model

The finite-size shift of the critical temperature is calculated by the example of the spherical model, with short- and long-range interactions, confined to the general geometryL ^d–d × ^d subject to periodic boundary conditions. The derived formula unifies in some sense all results found up to now.     

Charge Fluctuations in Finite Coulomb Systems

When described in a grand canonical ensemble, a finite Coulomb system exhibits charge fluctuations. These fluctuations are studied in the case of a classical (i.e., non-quantum) system with no macroscopic average charge. Assuming the validity of macroscopic electrostatics gives, on a three-dimensional finite large conductor of volume V, a mean square charge Q ² which goes as V ^1/3. More generally, in a short-circuited capacitor of capacitance C, made of two conductors, the mean square charge on one conductor is Q ²=TC, where T is the temperature and C the capacitance of the capacitor. The case of only one conductor in a grand canonical ensemble is obtained by removing the other conductor to infinity. The general formula is checked in the weak-coupling (Debye–Hückel) limit for a spherical capacitor. For two-dimensional Coulomb systems (with logarithmic interactions), there are exactly solvable models which reveal that, in some cases, macroscopic electrostatics is not applicable even for large conductors. This is when the charge fluctuations involve only a small number of particles. The mean square charge on one two-dimensional system alone, in the grand canonical ensemble, is expected to be, at most, one squared elementary charge.     

Gaussian fluctuations for the magnetization of Lee-Yang ferromagnets at zero external field

We consider the fluctuations of the block spin magnetization normalized by the square root of the considered number of spins in a block for Lee-Yang ferromagnets. It is established that the fluctuations are Gaussian when ^d at zero external field whenever the susceptibility is finite (i.e., above the critical temperature) and converges to the second derivative of the pressure at zero field. The validity of this fluctuation-dissipation condition is known to hold for a large class of Lee-Yang models, including, for instance, classical Heisenberg ferromagnets.     

Multi-instanton check of the relation between the prepotential F and the modulus u in N = 2 SUSY Yang-Mills theory

By examining multi-instantons in N = 2 supersymmetric SU(2) gauge theory, we derive, on very general grounds, and to all orders in the instanton number, a relationship between the prepotential

Full-size image

(Φ), and the coordinate on the quantum moduli space u = TrΦ². This relation was previously obtained by Matone in the context of the explicit Seiberg-Witten low-energy solution of the model. Our findings can be viewed as a multi-instanton check of the proposed exact results in supersymmetric gauge theory.     

Pressure Effects on Submicrosecond Phospholipid Dynamics Using a Long-Lived Fluorescence Probe

The effects of applied external hydrostatic pressure on submicrosecond lipid motions in DPPC⁴ bilayers have been examined using coronene (a long-lived planar fluorescent molecule) and DPH. Steady-state fluorescence emission anisotropy (EA) values () obtained for probe-labeled DPPC SUVs measured at different fixed temperatures above T _c as a function of increasing hydrostatic pressure reveal pressure-induced lipid phase transition profiles. For coronene-labeled samples, the observed lipid melt profiles are broad and shifted to higher midpoint EA pressure values (P _1/2) compared with corresponding DPH-labeled SUVs at the same temperature. The data suggest lipid motions occurring on the submicrosecond time scale, detected only by using a long-lived fluorescence probe, which occur well above the normally reported fluid–gel lipid phase transition. Slopes of the pressure-to-temperature equivalence plots (dP _1/2/dT = 39 bar/K) obtained for DPH-or coronene-labeled DPPC SUVs are identical within experimental error and reflect probe independence. For DPH, the slope of the P _1/2(T) plot provides the expected phase transition phospholipid volume change. However, intercept values (at P _1/2 = 1 bar) or apparent phase transition temperatures obtained from the equivalence plots for the two probes are not equal. Differences appear to arise due to the very disparate fluorescence lifetime values of the two probes, which result in rotational sensitivity of coronene to gel lipid volume fluctuations occurring during the extended time window provided by coronene fluorescence.     

Instanton Expansion of Noncommutative Gauge Theory in Two Dimensions

We show that noncommutative gauge theory in two dimensions is an exactly solvable model. A cohomological formulation of gauge theory defined on the noncommutative torus is used to show that its quantum partition function can be written as a sum over contributions from classical solutions. We derive an explicit formula for the partition function of Yang-Mills theory defined on a projective module for an arbitrary noncommutativity parameter which is manifestly invariant under gauge Morita equivalence. The energy observables are shown to be smooth functions of . The construction of noncommutative instanton contributions to the path integral is described in some detail. In general, there are infinitely many gauge inequivalent contributions of fixed topological charge, along with a finite number of quantum fluctuations about each instanton. The associated moduli spaces are combinations of symmetric products of an ordinary two-torus whose orbifold singularities are not resolved by noncommutativity. In particular, the weak coupling limit of the gauge theory is independent of and computes the symplectic volume of the moduli space of constant curvature connections on the noncommutative torus.     

Toward finite quantum field theories

The properties that make theN=4 super Yang-Mills theory free from ultraviolet divergences are (i) a universal coupling for gauge and matter interactions, (ii) anomaly-free representations, (iii) no charge renormalization, and (iv) if masses are explicitly introduced into the theory, then these are required to satisfy the mass-squared supertrace sum rule _s=0,1/2(–1)^2s+1(2s+1)M _s ² =0. FiniteN=2 theories are found to satisfy the above criteria. The missing member in this class of field theories are finite field theories consisting ofN=1 superfields. These theories are discussed in the light of the above finiteness properties. In particular, the representations of all simple classical groups satisfying the anomaly-free and no-charge renormalization conditions for finiteN=1 field theories are discussed. A consequence of these restrictions on the allowed representations is that anN=1 finiteSU (5)-based model of strong and electroweak interactions can contain at most five conventional families of quarks and leptons, a constraint almost compatible with the one deduced from cosmological arguments.