PT-symmetric kinks

Some kinks for non-Hermitian quantum field theories in 1+1 dimensions are constructed. A class of models where the soliton energies are stable and real are found. Although these kinks are not Hermitian, they are symmetric under PT transformations.

On the Dirac equation with PT-symmetric potentials in the presence of position-dependent mass

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Infrared degrees of freedom of Yang-Mills theory in the Schrodinger representation

We set up a new calculational framework for the Yang-Mills vacuum transition amplitude in the Schrodinger representation. After integrating out hard-mode contributions perturbatively and performing a gauge-invariant gradient expansion of the ensuing soft-mode action, a manageable saddle-point expansion for the vacuum overlap can be formulated. In combination with the squeezed approximation to the vacuum wave functional this allows for an essentially analytical treatment of physical amplitudes. Moreover, it leads to the identification of dominant and gauge-invariant classes of gauge field orbits which play the role of gluonic infrared (IR) degrees of freedom. The latter emerge as a diverse set of saddle-point solutions and are represented by unitary matrix fields. We discuss their scale stability, the associated virial theorem and other general properties including topological quantum numbers and action bounds. We then find important saddle-point solutions (most of them solitons) explicitly and examine their physical impact. While some are related to tunneling solutions of the classical Yang-Mills equation, i.e. to instantons and merons, others appear to play unprecedented roles. A remarkable new class of IR degrees of freedom consists of Faddeev-Niemi type link and knot solutions, potentially related to glueballs.

Pion structure in the instanton liquid model

The covariant quark model of the pion based on the effective nonlocal quark-hadron Lagrangian involving nonlocality induced by instanton fluctuations of the QCD vacuum is reviewed. Explicit gauge invariant formalism allows us to construct the conserved vector and axial currents and to demonstrate their consistency with the Ward-Takahashi identities and low-energy theorems. The spontaneous breaking of chiral symmetry results in the dynamic quark mass and the vertex of the quark-pion interaction, both momentum-dependent. The parameters of the instanton vacuum, the average size of the instantons, and the effective quark mass are expressed in terms of the vacuum expectation values of the lowest dimension quark-gluon operators and low-energy pion observables. The transition pion form factor for the processes gamma*gamma --> pi (0) and gamma*gamma* --> pi (0) is analyzed in detail. The kinematic dependence of the transition form factor at high momentum transfers allows one to determine the relationship between the light-cone amplitude of the quark distribution in the pion and the quark-pion vertex function. Its dynamic dependence implies that the transition form factor gamma*gamma --> pi (0) at high momentum transfers is acutely sensitive to the size of the nonlocality of nonperturbative fluctuations in the QCD vacuum. In the leading twist, the distribution amplitude and the distribution function of the valence quarks in the pion are calculated at a low normalization point of the order of the inverse average instanton size rho (-1)(c). The QCD results are evolved to higher momentum transfers and are in reasonable agreement with available experimental data on the pion structure.

Many-body theory for systems of composite hadrons

Many-body systems of composite hadrons are characterized by processes that involve the simultaneous presence of hadrons and their constituents. We briefly review several methods that have been devised to study such systems and present a novel method that is based on the ideas of mapping between physical and ideal Fock spaces. The method, known as the Fock-Tani representation, was invented years ago in the context of atomic physics problems and was recently extended to hadronic physics. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, Hermitian Hamiltonians with a clear physical interpretation are obtained. The use of the method in connection with the linked-cluster formalism to describe short-range correlations and quark deconfinement effects in nuclear matter is discussed. As an application of the method, an effective nucleon-nucleon interaction is derived from a constituent quark model and used to obtain the equation of state of nuclear matter in the Hartree-Fock approximation.

Neutrino mixing and the minimal 3-3-1 model

In the minimal 3-3-1 model charged leptons come in a nondiagonal basis. Moreover, the Yukawa interactions of the model lead to a non-hermitian charged lepton mass matrix. In other words, the minimal 3-3-1 model presents a very complex lepton mixing. In view of this we check rigorously if the possible textures of the lepton mass matrices allowed by the minimal 3-3-1 model can lead or not to the neutrino mixing required by the recent experiments in neutrino oscillation.

Mapping of composite hadrons into elementary hadrons and effective hadronic Hamiltonians

A mapping technique is used to derive in the context of constituent quark models effective Hamiltonians that involve explicit hadron degrees of freedom. The technique is based on the ideas of mapping between physical and ideal Fock spaces and shares similarities with the quasiparticle method of Weinberg. Starting with the Fock-space representation of single-hadron states, a change of representation is implemented by a unitary transformation such that composites are redescribed by elementary Bose and Fermi field operators in an extended Fock space. When the unitary transformation is applied to the microscopic quark Hamiltonian, effective, hermitian Hamiltonians with a clear physical interpretation are obtained. Applications and comparisons with other composite-particle formalisms of the recent literature are made using the nonrelativistic quark model. (C) 1998 Academic Press.

General unitary SU(1,1) TFD formulation

In this Letter we discuss a generalization for the thermal Bogoliubov transformation in the context of a Hermitian general SU(1,1) transformation generator. The TFD tilde conjugation rules are redefined using an appropriated Tomita-Takesaki modular operator. (C) 2003 Elsevier B.V. All rights reserved.

QCD glueball sum rules revisited

We discuss several key problems of conventional QCD glueball sum rules in the spin-0 channels and show how they are overcome by nonperturbative Wilson coefficients. The nonperturbative contributions originate from direct instantons and, in the pseudoscalar channel, additionally from topological charge screening. The treatment of the direct-instanton sector is based on realistic instanton size distributions and renormalization at the operator scale. The resulting predictions for spin-0 glueball properties as well as their implications for experimental glueball searches are discussed.

Topological charge screening and pseudoscalar glueballs

Topological charge screening in the QCD vacuum is found to provide crucial nonperturbative contributions to the short-distance expansion of the pseudoscalar (0-+) glueball correlator. The screening contributions enter the Wilson coefficients and are an indispensable complement to the direct instanton contributions. They restore consistency with the anomalous axial Ward identity and remedy several flaws in the 0-+ glueball sum rules caused by direct instantons in the absence of screening (lack of resonance signals, violation of the positivity bound and of the underlying low-energy theorem). The impact of the finite width of the instanton size distribution and the (gauge-invariant) renormalization of the instanton contributions are also discussed. New predictions for the 0-+ glueball mass and decay constant are presented.

The higher grading structure of the WKI hierarchy and the two-component short pulse equation

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)

Abelian-Higgs and vortices from ABJM: towards a string realization of AdS/CMT

Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq)

Self-dual hopfions

We construct static and time-dependent exact soliton solutions with nontrivial Hopf topological charge for a field theory in 3 + 1 dimensions with the target space being the two dimensional sphere S(2). The model considered is a reduction of the so-called extended Skyrme-Faddeev theory by the removal of the quadratic term in derivatives of the fields. The solutions are constructed using an ansatz based on the conformal and target space symmetries. The solutions are said self-dual because they solve first order differential equations which together with some conditions on the coupling constants, imply the second order equations of motion. The solutions belong to a sub-sector of the theory with an infinite number of local conserved currents. The equation for the profile function of the ansatz corresponds to the Bogomolny equation for the sine-Gordon model.

Grassmannian and bosonic Thirring models with jump defects

In this paper we discuss the Lax formulation of the Grassmannian and Bosonic Thirring models in the presence of jump defects. For the Grassmannian case, the defect is described by Backlund transformation which is responsible for preserving the integrability of the model. We then propose an extension of the Backlund transformation for the Bosonic Thirring model which is verified by some Backlund transitions like vacuum-one soliton, one soliton-one soliton, one soliton-two solitons and two solitons-two solitons. The Lax formulation within the space split by the defect leads to the integrability of Bosonic Thirring model with jump defects.

Fluctuating dimension in a discrete model for quantum gravity based on the spectral principle

The spectral principle of Connes and Chamseddine is used as a starting point to define a discrete model for Euclidean quantum gravity. Instead of summing over ordinary geometries, we consider the sum over generalized geometries where topology, metric, and dimension can fluctuate. The model describes the geometry of spaces with a countable number n of points, and is related to the Gaussian unitary ensemble of Hermitian matrices. We show that this simple model has two phases. The expectation value , the average number of points in the Universe, is finite in one phase and diverges in the other. We compute the critical point as well as the critical exponent of . Moreover, the space-time dimension delta is a dynamical observable in our model, and plays the role of an order parameter. The computation of is discussed and an upper bound is found, < 2.