Unitarity Bound of the Wave Function Renormalization Constant

The wave function renormalization constant $Z$, the probability to find the bare particle in the physical particle, usually satisfies the unitarity bound $0 \leq Z \leq 1$ in field theories without negative metric states. This unitarity bound implies the positivity of the anomalous dimension of the field in the one-loop approximation. In nonlinear sigma models, however, this bound is apparently broken because of the field dependence of the canonical momentum. The contribution of the bubble diagrams to the anomalous dimension can be negative, while the contributions from more than two particle states satisfies the positivity of the anomalous dimension as expected. We derive the genuine unitarity bound of the wave function renormalization constant.Comment: 8 pages, 2 figures, comments adde

Normal Coordinates in Kahler Manifolds and the Background Field Method

Riemann normal coordinates (RNC) are unsuitable for Kahler manifolds since they are not holomorphic. Instead, Kahler normal coordinates (KNC) can be defined as holomorphic coordinates. We prove that KNC transform as a holomorphic tangent vector under holomorphic coordinate transformations, and therefore they are natural extensions of RNC to the case of Kahler manifolds. The KNC expansion provides the manifestly covariant background field method preserving the complex structure in supersymmetric nonlinear sigma models

Latent heat in the chiral phase transition

The chiral phase transition at finite temperature and density is discussed in the framework of the QCD-like gauge field theory. The thermodynamical potential is investigated using a variational approach. Latent heat generated in the first-order phase transition is calculated. It is found that the latent heat is enhanced near the tricritical point and is more than several hundred MeV per quark.Comment: 6 pages, 3 figure

Chiral phase transition at high temperature in the QCD-like gauge theory

The chiral phase transition at high temperature is investigated using the effect ive potential in the framework of the QCD-like gauge theory with a variational a pproach. We have a second order phase transition at $T_c=136$MeV. We also investigate numerically the temperature dependence of condensate, $f_\pi$ a nd $a_2(T)$(coefficient of the quadratic term in the effective potential) and es timate the critical exponents of these quantities.Comment: 12 pages,7 figure

Self-consistent nonperturbative anomalous dimensions

A self-consistent treatment of two and three point functions in models with trilinear interactions forces them to have opposite anomalous dimensions. We indicate how the anomalous dimension can be extracted nonperturbatively by solving and suitably truncating the topologies of the full set of Dyson-Schwinger equations. The first step requires a sensible ansatz for the full vertex part which conforms to first order perturbation theory at least. We model this vertex to obtain typical transcendental equations between anomalous dimension and coupling constant $g$ which coincide with know results to order $g^4$.Comment: 15 pages LaTeX, no figures. Requires iopart.cl

Non-Abelian Walls in Supersymmetric Gauge Theories

The Bogomol'nyi-Prasad-Sommerfield (BPS) multi-wall solutions are constructed in supersymmetric U(N_C) gauge theories in five dimensions with N_F(>N_C) hypermultiplets in the fundamental representation. Exact solutions are obtained with full generic moduli for infinite gauge coupling and with partial moduli for finite gauge coupling. The generic wall solutions require nontrivial configurations for either gauge fields or off-diagonal components of adjoint scalars depending on the gauge. Effective theories of moduli fields are constructed as world-volume gauge theories. Nambu-Goldstone and quasi-Nambu-Goldstone scalars are distinguished and worked out. Total moduli space of the BPS non-Abelian walls including all topological sectors is found to be the complex Grassmann manifold SU(N_F) / [SU(N_C) x SU(N_F-N_C) x U(1)] endowed with a deformed metric.Comment: 62 pages, 17 figures, the final version in PR

Scalar-Quark Systems and Chimera Hadrons in SU(3)_c Lattice QCD

Light scalar-quarks \phi (colored scalar particles or idealized diquarks) and their color-singlet hadronic states are studied with quenched SU(3)_c lattice QCD in terms of mass generation in strong interaction without chiral symmetry breaking. We investigate ``scalar-quark mesons'' \phi^\dagger \phi and ``scalar-quark baryons'' \phi\phi\phi which are the bound states of scalar-quarks \phi. We also investigate the bound states of scalar-quarks \phi and quarks \psi, i.e., \phi^\dagger \psi, \psi\psi\phi and \phi\phi\psi, which we name ``chimera hadrons''. All the new-type hadrons including \phi are found to have a large mass even for zero bare scalar-quark mass m_\phi=0 at a^{-1}\simeq 1GeV. We find that the constituent scalar-quark and quark picture is satisfied for all the new-type hadrons. Namely, the mass of the new-type hadron composed of m \phi's and n \psi's, M_{{m}\phi+{n}\psi}, satisfies M_{{m}\phi+{n}\psi}\simeq {m} M_\phi +{n} M_\psi, where M_\phi and M_\psi are the constituent scalar-quark and quark mass, respectively. M_\phi at m_\phi=0 estimated from these new-type hadrons is 1.5-1.6GeV, which is larger than that of light quarks, M_\psi\simeq 400{\rm MeV}. Therefore, in the systems of scalar-quark hadrons and chimera hadrons, scalar-quarks acquire large mass due to large quantum corrections by gluons. Together with other evidences of mass generations of glueballs and charmonia, we conjecture that all colored particles generally acquire a large effective mass due to dressed gluon effects.Comment: 9 pages, 9 figure