International Journal of Modern Physics A

Virtual effects induced by new physics in rare Z decays are reviewed. Since the expected sensitivity of the giga-Z linear collider is of the order of 10^-8, we emphasize the importance of any new physics effect that gives a prediction above this limit. It is also pointed out that an improvement on the known experimental constraints on rare Z decays will provide us with a critical test of the validity of the standard model at the loop level.

We present a pedagogical review of particle physics models that are based on the noncommutativity of space–time, , with specific attention to the phenomenology these models predict in particle experiments either in existence or under development. We summarize results obtained for high energy scattering such as would occur, for example, in a future e⁺e^- linear collider with , as well as low energy experiments such as those pertaining to elementary electric dipole moments and other CP violating observables, and finally comment on the status of phenomenological work in cosmology and extra dimensions.

Two-dimensional SU(N) Yang–Mills theory is known to be equivalent to a string theory, as found by Gross in the large N limit, using the 1/N expansion. Later it was found that even a generalized YM theory leads to a string theory of the Gross type. In the standard YM theory case, Douglas and others found the string Hamiltonian describing the propagation and the interactions of states made of strings winding on a cylindrical space–time. We address the problem of finding a similar Hamiltonian for the generalized YM theory. As in the standard case we start by writing the theory as a theory of free fermions. Performing a bosonization, we express the Hamiltonian in terms of the modes of a bosonic field, that are interpreted as in the standard case as creation and destruction operators for states of strings winding around the cylindrical space–time. The result is similar to the standard Hamiltonian, but with new kinds of interaction vertices.

We introduce a matrix model for noncommutative gravity, based on the gauge group U(2)⊗U(2). The vierbein is encoded in a matrix Y_μ, having values in the coset space U(4)/(U(2)⊗U(2)), while the spin connection is encoded in a matrix X_μ, having values in U(2)⊗U(2). We show how to recover the Einstein equations from the θ→0 limit of the matrix model equations of motion. We stress the necessity of a metric tensor, which is a covariant representation of the gauge group in order to set up a consistent second order formalism. We finally define noncommutative gravitational instantons as generated by U(2)⊗U(2) valued quasi-unitary operators acting on the background of the matrix model. Some of these solutions have naturally self-dual or anti-self-dual spin connections.

We discuss phenomenological tests for the frozen infrared behavior of the running coupling constant and gluon propagators found in some solutions of Schwinger–Dyson equations of the gluonic sector of QCD. We verify that several observables can be used in order to select the different expressions of α_s found in the literature. We test the effect of the nonperturbative coupling in the τ-lepton decay rate into nonstrange hadrons, in the ρ vector meson helicity density matrix that are produced in the χ_c2→ρρ decay, in the photon to pion transition form factor, and compute the cross-sections for elastic proton–proton scattering and exclusive ρ production in deep inelastic scattering. These quantities depend on the infrared behavior of the coupling constant at different levels, we discuss the reasons for this dependence and argue that the existent and future data can be used to test the approximations performed to solve the Schwinger–Dyson equations and they already seem to select one specific infrared behavior of the coupling.

We study an effective theory of QCD in which the fundamental variables are dual magnetic potentials coupled to the monopole field. Dual dynamics are then used to explain the properties of QCD vacuum at zero temperature as well as at finite temperatures. At zero temperature, the color confinement is realized through the dynamical breaking of magnetic symmetry, which leads to the magnetic condensation of QCD vacuum. The flux tube structure of SU(2) QCD vacuum is investigated by solving the field equations in the low energy regimes of the theory, which guarantees dual superconducting nature of the QCD vacuum. The QCD phase transition at finite temperature is studied by the functional diagrammatic evaluation of the effective potential on the one-loop level. We then obtained analytical expressions for the vacuum expectation value of the condensed monopoles as well as the masses of glueballs from the temperature dependent effective potential. These nonperturbative parameters are also evaluated numerically and used to determine the critical temperature of the QCD phase transition. Finally, it is shown that near the critical temperature (T_c≃0.195 GeV), continuous reduction of vacuum expectation value (VEV) of the condensed monopoles caused the disappearance of vector and scalar glueball masses, which brings a second order phase transition in pure SU(2) gauge QCD.

The uniformity of the decomposition law, for a family ℱ of Lie algebras which includes the exceptional Lie algebras, of the tensor powers ad^⊗n of their adjoint representations ad is now well known. This paper uses it to embark on the development of a unified tensor calculus for the exceptional Lie algebras. It deals explicitly with all the tensors that arise at the n=2 stage, obtaining a large body of systematic information about their properties and identities satisfied by them. Some results at the n=3 level are obtained, including a simple derivation of the dimension and Casimir eigenvalue data for all the constituents of ad^⊗3. This is vital input data for treating the set of all tensors that enter the picture at the n=3 level, following a path already known to be viable for .

The special way in which the Lie algebra conforms to its place in the family ℱ alongside the exceptional Lie algebras is described.