Canonical formulation of the spherically symmetric einstein-Yang-Mills-Higgs system for a general gauge group

The dynamics of the spherically symmetric system of gravitation interacting with scalar and Yang-Mills fields is presented in the context of the canonical formalism. The gauge group considered is a general (compact and semisimple) N parameter group. The scalar (Higgs) field transforms according to an unspecified M-dimensional orthogonal representation of the gauge group. The canonical formalism is based on Dirac's techniques for dealing with constrained hamiltonian systems. First the condition that the scalar and Yang-Mills fields and their conjugate momenta be spherically symmetric up to a gauge is formulated and solved for global gauge transformations, finding, in a general gauge, the explicit angular dependence of the fields and conjugate momenta. It is shown that if the gauge group does not admit a subgroup (locally) isomorphic to the rotation group, then the dynamical variables can only be manifestly spherically symmetric. If the opposite is the case, then the number of allowed degrees of freedom is connected to the angular momentum content of the adjoint representation of the gauge group. Once the suitable variables with explicit angular dependence have been obtained, a reduced action is derived by integrating away the angular coordinates. The canonical formulation of the problem is now based on dynamical variables depending only on an arbitrary radial coordinate r and an arbitrary time coordinate t. Besides the gravitational variables, the formalism now contains two pairs of N-vector variables (R, π_r), (Θ, π_Θ), corresponding to the allowed Yang-Mills degrees of freedom and one pair of M-vector variables, (h, π_h), associated with the original scalar field. The reduced Hamiltonian is invariant under a group of r-dependent gauge transformations such that R plays the role of the gauge field (transforming in the typically inhomogeneous way) and in terms of which the gauge covariant derivatives of Θ and h naturally appear. No derivatives of R appear in the Hamiltonian and the gauge freedom allows us to define a gauge in which R is zero. Also the r and t coordinates are fixed in a way consistent with the equations of motion. Some nontrivial static solutions are found. One of these solutions is given in closed form; it is singular and corresponds to a generalization of the singular solution found in the literature with different degrees of generality and the geometry is described by the Reissner-Nordström metric. The other solution is defined through its asymptotic behavior. It generalizes to curved space the finite energy solution discyssed by Julia and Zee in flat space.     

The spherically symmetric Standard Model with gravity

Spherical reduction of generic four-dimensional theories is revisited. Three different notions of “spherical symmetry” are defined. The following sectors are investigated: Einstein-Cartan theory, spinors, (non-)abelian gauge fields and scalar fields. In each sector a different formalism seems to be most convenient: the Cartan formulation of gravity works best in the purely gravitational sector, the Einstein formulation is convenient for the Yang-Mills sector and for reducing scalar fields, and the Newman-Penrose formalism seems to be the most transparent one in the fermionic sector. Combining them the spherically reduced Standard Model of particle physics together with the usually omitted gravity part can be presented as a two-dimensional (dilaton gravity) theory.     

Exact solution of Poincaré gauge field equations of gravity with torsion

Under empty, static, and spherically symmetric conditions we find an exact metric solution of the Poincaré gauge field equations. The Schwarzschild metric solution is contained in the solution and we also obtain new gauge correction termsr ^–1 andr ² lnr.     

On spherically symmetric fields with dynamic torsion in gauge theories of gravitation

Within the framework of the Poincaré gauge field theory of gravity, the general gravitational Lagrangian coupled to the electromagnetic field is investigated. We treat the case of a static, spherically symmetric field with space reflection invariance. The exact solutions presented will be generated by a double-duality ansatz for the curvature. The Reissner-Nordström metric is singled out within a class of Lagrangians admitting an asymptotically flat metric.     

K–K excitations on as “primary” superfields

We show that the K–K spectrum of IIB string on is described by “twisted chiral” superfields, naturally described in “harmonic superspace”, obtained by taking suitable gauge singlets polynomials of the D3-brane boundary superconformal field theory.To each p-order polynomial is associated a massive K–K short representation with states. The quadratic polynomial corresponds to the “supercurrent multiplet” describing the “massless” bulk graviton multiplet.     

Comparative Regge analysis of Λ,ΣΛ(1520) and Θ<Superscript>+</Superscript> production in γp,πp and pp reactions

Using the Quark-Gluon Strings Model --combined with Regge phenomenology-- we perform a comparative analysis of Λ, Σ⁰, Λ(1520) and Θ⁺ production in binary reactions induced by photon, pion and proton beams on the nucleon. We find that the existing experimental data on the γp↦K⁺Λ differential and total cross-sections can be described very well by the model for photon energies 1-16 GeV and - t < 2 GeV² assuming a dominant contribution of the K^* Regge trajectory. Moreover, using the same parameters we also reproduce the total γp↦K⁺Σ⁰ and γp↦K⁺Λ(1520) cross-sections suggesting a “universality” of the Regge model. In order to check the consistency of the approach we evaluate the differential and total cross-sections for the reaction π^-p↦K⁰Λ which is also found to be dominated by the K^* Regge trajectory. Using the apparent “universality” of the Regge model we extend our scheme to the analysis of the binary reactions γp↦¯⁰Θ⁺, π^-p↦K^-Θ⁺ and pp↦Σ⁺Θ⁺ as well as the exclusive and inclusive Θ⁺ production in the reactions pp↦p¯⁰Θ⁺ and pp↦Θ⁺X. Our detailed studies demonstrate that Θ⁺ production does not follow the “universality” principle, thus suggesting an essentially different internal structure of the exotic baryon relative to conventional hyperons or hyperon resonances.     

Asymptotically de Sitter and anti-de Sitter black holes with confining electric potential

We study gravity interacting with a special kind of QCD-inspired nonlinear gauge field system which earlier was shown to yield confinement-type effective potential (the “Cornell potential”) between charged fermions (“quarks”) in flat space-time. We find new static spherically symmetric solutions generalizing the usual Reissner-Nordström-de Sitter and Reissner-Nordström-anti-de Sitter black holes with the following additional properties: (i) appearance of a constant radial electric field (in addition to the Coulomb one); (ii) novel mechanism of dynamical generation of cosmological constant through the non-Maxwell gauge field dynamics; (iii) appearance of confining-type effective potential in charged test particle dynamics in the above black hole backgrounds.     

Yang-Mills Fields as Optical Media

A geometrization of the Yang-Mills field, by which an SU(2) gauge theorybecomes equivalent to a 3-space geometry—or optical system—is examined. Ina first step, ambient space remains Euclidean and current problems on flat spacecan be looked at from a new point of view. The Wu-Yang ambiguity, for example,appears related to the multiple possible torsions of distinct metric-preservingconnections. In a second step, the ambient space also becomes curved. In thegeneric case, the strictly Riemannian metric sector plays the role of an arbitraryhost space, with the gauge potential represented by a contorsion. For some fieldconfigurations, however, it is possible to obtain a purely metric representation.In those cases, if the space is symmetric homogeneous, the Christoffel connectionsare automatically solutions of the Yang-Mills equations.     

Pohlmeyer reduction of superstring sigma model

Motivated by a desire to find a useful 2d Lorentz-invariant reformulation of the AdS₅×S⁵ superstring world-sheet theory in terms of physical degrees of freedom we construct the “Pohlmeyer-reduced” version of the corresponding sigma model. The Pohlmeyer reduction procedure involves several steps. Starting with a coset space string sigma model in the conformal gauge and writing the classical equations in terms of currents one can fix the residual conformal diffeomorphism symmetry and kappa-symmetry and introduce a new set of variables (related locally to currents but non-locally to the original string coordinate fields) so that the Virasoro constraints are automatically satisfied. The resulting equations can be obtained from a Lagrangian of a non-Abelian Toda type: a gauged WZW model with an integrable potential coupled also to a set of 2d fermionic fields. A gauge-fixed form of the Pohlmeyer-reduced theory can be found by integrating out the 2d gauge field of the gauged WZW model. The small-fluctuation spectrum near the trivial vacuum contains 8 bosonic and 8 fermionic degrees of freedom with equal mass. We conjecture that the reduced model has world-sheet supersymmetry and is ultraviolet-finite. We show that in the special case of the AdS₂×S² superstring model the reduced theory is indeed supersymmetric: it is equivalent to the N=2 supersymmetric extension of the sine-Gordon model.     

From massive gravity to modified general relativity

Massive gravity which has been constructed from a cohomological formulation of gauge invariance by means of the descent equations is here investigated in the classical limit. Gauge invariance requires a vector-graviton field v coupled to the massive tensor field h _μν . In the limit of vanishing graviton mass the v-field does not decouple. On the classical level this leads to a modification of general relativity. The contribution of the v-field to the energy-momentum tensor can be interpreted as dark matter density and pressure. We solve the modified field equations in the simplest spherically symmetric geometry.     

Quark confinement in 2+1 dimensional pure Yang-Mills theory

We report some progress on the quark confinement problem in 2 + 1 dim. pure Yang-Mills theory, using Euclidean instanton methods. The instantons are regularized Wu-Yang ‘monopoles’, whose long range Coulomb field is screened by collective effects. Such configurations are stable to small perturbations unlike the case of singular, undressed monopoles. Using exact non-perturbative results for the 3-dim. Coulomb gas, where Debye screening holds for arbitrarily low temperatures, we show in a self-consistent way that a mass gap is dynamically generated in the gauge theory. The mass gap also determines the size of the monopoles. We also identify the disorder operator of the model in terms of the Sine-Gordon field of the Coulomb gas and hence obtain a dual representation whose symmetry is the centre ofSU(2).     

SO q (4) quantum mechanics

In this paper we extend our previously discovered exact solution for an SU(2) Yang-Mills-Higgs theory, to the general group SU(N+1). Using the first-order formalism of Bogomolny, an exact, spherically symmetric solution for the gauge and scalar fields is found. This solution is similar to the Schwarzschild solution of general relativity, in that the gauge and scalar fields become infinite on a spherical shell of radiusr ₀=K. However in the Schwarzschild case the singularity at the event horizon is a coordinate singularity while for the present solution the singularity is a true singularity. It is speculated that this solution may give a confinement mechanism for non-Abelian gauge theories, since any particle which carries the SU(N+1) charge would become permanently trapped inside the regionr<r ₀.     

A spherically symmetric vacuum solution of the quadratic Poincaré gauge field theory of gravitation with newtonian and confinement potentials

We derive a stationary spherically symmetric vacuum solution in the framework of the Poincaré gauge field theory with a recently proposed quadratic lagrangian. We find a metric of the Schwarzschild-de Sitter type, both torsion and curvature are non vanishing, with torsion proportional to the mass and curvature proportional to the strong coupling constant κ. The metric exhibits two pieces, a newtonian potential describing the gravitational behavior of macroscopic matter, and a confining potential ～κr² presumably related to the strong-interaction properties of hadrons. To our knowledge this is a new feature of a classical solution of a Yang-Mills type gauge theory.     

Classical initial conditions in high energy nucleus-nucleus collisions

An iterative proceedure is proposed to compute the classical gauge field produced in the collision of two heavy nuclei. The leading order is obtained by linearizing the Yang-Mills equations in the light-cone gauge, and provides a simple formula for gluon production in nucleus-nucleus collisions. At this order k_t–factorization breaks down.     

Two-dimensional Yang-Mills theory in the leading 1N expansion

Recent controversies about the gauge invariance of the two-dimensional SU(N) Yang-Mills theory in the 't Hooft limit of large N are resolved. The fermion (quark) propagator is found explicitly, and is qualitatively different from those in the previous literature.     

Gauge invariant geometric variables for Yang-Mills theory

In a previous publication, local gauge invariant geometric variables were introduced to describe the physical Hilbert space of Yang-Mills theory. In these variables, the electric energy involves the inverse of an operator which can generically have zero-modes, and thus its calculation is subtle. In the present work, we resolve these subtleties by considering a small deformation in the definition of these variables, which in the end is removed. The case of spherical configurations of the gauge invariant variables is treated in detail, as well as the inclusion of infinitely heavy point color sources, and the expression for the associated electric field is found explicitly. These spherical geometries are seen to correspond to the spatial components of instanton configurations. The related geometries corresponding to Wu-Yang monopoles and merons are also identified.     

Effective spin susceptibility, electron mass and Landé factor in two-dimensional (2D) Si inversion layers

We have studied the silicon (Si) band-structure, electron–electron and electron-ionized donor interaction effects on our accurate and approximate results (AcR and ApR) for renormalized effective spin susceptibitity (RESS), electron mass (EEM), Landé factor and spin polarization in the impure 2D Si (electron system), showing that:(i) our ApR, being strongly deviated from our AcR, reproduces approximately all the data obtained recently by Pudalov et al. (Phys. Rev. Lett. 88 (2002) 196404) [in particular, RESS =4.7 at the critical value of Wigner–Seitz radius r_s: r_s=r_c≈8.5 at which occur the “apparent” metal–insulator transition (MIT)] and can also be compared with other ApRs found in the recent literature,(ii) both the RESS and EEM produce physical singularities at the same critical value: r_s=r_c11.05661 (weakly disordered samples) at which occurs the “true” MIT; the existence of such two “apparent and true” critical values in this impure system agrees with a recent discussion by Abrahams et al. (Rev. Mod. Phys. 73 (2001) 251), and(iii) at r_s=r_c=8.5, at which occurs the “apparent” MIT, our AcR for effective spin polarization and the corresponding result, obtained using a disordered Hubbard model and a determinant quantum Monte Carlo method by Denteneer and Scalettar (Phys. Rev. Lett. 90 (2003) 246401), both give the same result: ξ_eff.=ξ_c0.31 at B0.4 T, which is found to be lower than the critical parallel magnetic field for full spin polarization, B_c=1.29 T, supporting thus the existence of such an “apparent” MIT.