Spectrum calculations in the lattice Georgi-Glashow model

Numerical evidence is found for the appearance of a massless vector state, the “photon”, in the broken phase of the lattice Georgi-Glashow model. Data is also presented for the lowest-lying scalar mass in the theory. Our simulations indicate that the transition between symmetric and broken phases is weakly first order for a wide range of couplings.     

The lattice Georgi-Glashow model in three dimensions

We find the phase diagram of the 3-DSU(2) lattice gauge-Higgs model with the scalar fields transforming as triplets underSU(2). The model is studied for several values of λ, the Higgs self-coupling. When λ is sufficiently small, the Higgs phase transition continues to new regions of the coupling constant space, due to the radial fluctuations.     

Investigation of the vacuum structure of the Georgi-Glashow model on the lattice

In this paper the BKS kernels of BRST bosonic strings are given. And from the kernels the relationships between geometric quantization and path integral quantization of bosonic strings with BRST symmetry are established. At the classical level, we also prove that the symplectic form in the phase space of bosonic strings is BRST invariant and nondegenerate.     

Instanton induced chiral symmetry breaking in extended QCD model

A mechanism for instanton induced chiral symmetry breaking in an extended QCD model (QCD with fundamental scalars) is proposed to describe quarks and gluons inside a baryon. The model Lagrangian that we use has the same symmetry properties as QCD. The scalar fields are shown to develop vacuum expectation values in the instanton background and generate masses for the three generation of quarks. The minimization condition is also used to break the flavour symmetry to make the -quark heavier that the and quarks. Received: 16 August 1996 / Revised version: 15 October 1997 / Published online: 26 February 1998     

Instanton constituents in the O(3) model at finite temperature

It is shown that instantons in the O(3) model at finite temperature consist of fractional charge constituents and the (topological) properties of the latter are discussed.     

Instanton screening in the nonperturbative QCD

The gluon field screening in the stochastic vacuum of gluodynamics is studied. The effective action is derived for the instanton interacting with nonperturbative fields. Quantum nonperturbative effects are shown to affect greatly the shape of instanton. The power asymptotics x ⁻² of the classical “instanton’s profile function” at large distances is replaced due to these effects by Airy function asymptotics.     

On the Instanton R-matrix

We discuss the chiral anomaly for a Weyl field in a curved background and show that a novel index theorem for the Lorentzian Dirac operator can be applied to describe the gravitational chiral anomaly. A formula for the total charge generated by the gravitational and gauge field background is derived directly in Lorentzian signature and in a mathematically rigorous manner. It contains a term identical to the integrand in the Atiyah–Singer index theorem and another term involving the \({\eta}\)-invariant of the Cauchy hypersurfaces.     

Instanton solution in tachyon cosmology

We find an exact classical solution in Euclidean gravity coupled to a scalar field with a particular form of potential commonly used in tachyon cosmology. This solution represents a tunneling between two vacua.     

Instanton vacuum in thermal QCD

The effects of instanton-anti-instanton interactions in high-temperature QCD with colour SU(2) are studied with and without quarks. The instanton potential proves to have no repulsive core, thus creating troubles with the definition of nonperturbative contributions to physical quantities. Also the chiral condensate is calculated, and it is shown to vanish if number of quark flavoursN _f≧2, whereas forN _f=1 it is nonzero for the arbitrary high temperature.     

Instanton induced interactions

Quarks interact under the influence of instantons. These interactions affect the wavefunctions of pions and nucleons and produce differences in the transverse momentum distributions of the up and down quarks within a nucleon.     

Instanton effects in supersymmetric theories

We calculate some simplest n-point functions in supersymmetric Yang-Mills theories contributed by instantons. The result is not vanishing and we discuss some implications of this. In particular, the dynamics of the supersymmetric theories must exhibit some unusual features.     

Instanton approximation to the graded nonlinear sigma model for the integer quantum hall effect

We construct the multi-instanton solutions for the graded nonlinear σ model with symmetry U(1,1/2)/U(1/1) ⊗ U(1/1), and we calculate the quantum fluctuations around these solutions. The determinant of the fluctuation operator for a fixed multi-instanton solution turns out to be UV finite. However, the integration over instanton parameters contains an integral, ∫d|a| |a|⁻³, over the size, |a|, of each instanton, which is quadratically singular at |a|=0. It is shown that these quadratic divergences cancel exactly in the calculation of all Green functions. The applicability of the present results to the integer quantum Hall effect is discussed.     

Instanton in disordered Peierls systems

We study disordered Peierls systems described by the fluctuating gap model. We show that the typical electron states with energies lying deep inside the pseudogap are localized near large disorder fluctuations (instantons), which have the form of a soliton-antisoliton pair. Using the “saddle-point” method we obtain the average density of states and the average optical absorption coefficient at small energy.     

Instanton interactions in dense-matter QCD

A Coulomb gas representation of dense-matter QCD is derived from a dual transformation of the low-energy effective Lagrangian. The point-like charges Q=±1 of the gas are identified with the instantons and anti-instantons of such topological charges. An instanton repels another instanton with the same force as it attracts an anti-instanton, in contrast to the semiclassical interaction.     

Instanton effects in meson spectroscopy

In this contribution, the results on the spectra and semileptonic decays of light and heavy mesons in a relativistic constituent quark model incorporating a confinement potential as well as a residual interaction induced by instantons are reported.     

Instanton effects in supersymmetric gauge theories

We investigate how in supersymmetric gauge theories non-perturbative effects are able to generate non-trivial vacuum properties otherwise forbidden by perturbative non-renormalization theorems. This conclusion can be reliably drawn since the constancy of certain Green functions — due to supersymmetry (SUSY) — allows one to connect vacuum-dominated large distances with short-distance behaviour which is reliably computed by instanton methods. In all the cases we discuss (without matter, with massive or massless matter in real representations and, finally, with matter in complex representations) instanton calculations imply the occurrence of a variety of condensates. For the pure SUSY gauge theory, a gluino condensate induces the spontaneous breaking of Z_2N. For massive super-quantum chromodynamics (SQCD) we find a peculiar mass dependence of matter condensates whose origin is traced to mass singularities of non-zero mode instanton contributions. These contributions force the massless limit of SQCD to differ from the strictly massless case, in which the spontaneous breaking of chiral symmetries is induced. Inconsistency with an anomaly equation forces either infinite matter condensates or spontaneous SUSY breaking in the massless cases. For non-constant Green functions, instantons are shown to provide new calculable short-distance singularities of an obvious non-perturbative nature.     

Instanton constraints and renormalization

The renormalization is investigated of one-loop quantum fluctuations around a constrained instanton in ?⁴-theory with negative coupling. It is found that the constraint should be renormalized also. This indicates that in general only renormalizable constraints are permitted.     

Instanton effects in the decay of scalar mesons

We show that instanton effects may play an important role in the decay of scalar mesons into two pseudoscalars. Particularly the branching ratios of two meson decays of the f₀(1500), which is considered as a glue-ball candidate, are compatible with an ordinary q -structure of this resonance and a small positive SU(3) mixing angle, in agreement with a result from a recent calculation of the spectrum with the same instanton-induced force. Predictions for the a₀(1450)-branching ratios are made.