Local field theory of the dual string

We develop a (classical) local field theory which contains as a special solution the (classical) dual string recently discussed by Goddard, Goldstone, Rebbi and Thorn. The basic field is a gauge field F_μν(x), and the Lagrangian is given by $\text{(}\text{?1}\text{2α'}\text{)√F}{}^2$. We treat the case of closed strings (corresponding to the Shapiro-Virasoro model) where F_μν can be expressed in terms of potentials A_μ. Quantization of F_μν is briefly discussed, but a more thorough discussion is postponed.     

Dynamical properties of the vacuum in non-abelian field theories with and without supersymmetry

In QCD with massless quarks, the effective potential for the color singlet operator (F_μν^a)² can be constructed by the use of the trace anomaly equation and tells us that magnetic gluon condensation, 〈0|(F_μν^a)²|0〉 > 0, occurs. When the method is applied to supersymmetric QCD, however, it gives us a puzzle; the gluons condense with negative energy density, and supersymmetry is broken in a pathological manner with the appearance of a negatively normed Nambu-Goldstone fermion. Spurred on by this observation, we examine in detail the properties of the vacuum for the super (and ordinary) O(N) non-linear σ model in two dimensions for which a similar puzzling situation occurs with regard to the lagrangian condensate. We find, in particular, that (i) the chiral condensate plays a crucial role in resolving the puzzle and that (ii) it is the nature of the response of the lagrangian condensate to the test charge, not the sign or the magnitude of the condensate itself, that determines the phase of the system. Implications of these results for (super) QCD, including an unconventional possibility of “electric” gluon condensation, are discussed.     

In search of scalar gluonium

We discuss a scalar meson coupled strongly to gluons. Radiative decays of the J/ψ are taken as a source of gluons so that our aim is to calculate Γ(J/ψ→σγ), where σ is the presumed scalar gluonium. We use QCD sum rules to find both 〈0|α_sG_μν^aG_μν^a|σ〉 (where G_μν^a is the gluon field strength tensor) and Γ(J/ψ→σγ) in terms of 〈0|α_sG_μν^aG_μν^a|σ〉. The final prediction for the width is expected to be valid within a factor of two and gives $\text{Γ(}\text{J}\text{/ψ→σγ→}\text{two pions in S-wave}\text{+ γ) ? 25}\text{eV for}\text{m}{}_{\mathrm{\sigma }}\text{= 700}\text{MeV}$. Non-perturbative QCD naturally explains the observed asymmetry between scalar and pseudoscalar states in the radiative decays of the J/ψ. Some general remarks on gluonium in QCD are made.     

Vacuum of the quantum Yang-Mills theory and magnetostatics

It is argued that since in asymptotically free Yang-Mills theories the quantum ground state is not controlled by perturbation theory, there is no a priori reason to believe that individual orbits corresponding to minima of the classical action dominate the Euclidean functional integral. To examine and classify the vacua of the quantum gauge theory, we propose an effective action in which the gauge field coupling constant g is replaced by the effective coupling $\text{g}\text{(t), t =}\text{ln}\text{[}\text{F}{}_{\mathrm{\mu \nu }}{}^{\mathrm{a}}\text{)}{}^2\text{μ}{}^4\text{]}$. The vacua of this model correspond to paramagnetism and perfect paramagnetism, for which the gauge field is F_μν^a = 0, and ferromagnetism, for which (F_μν^a)² = λ², i.e. spontaneous magnetization of the vacuum occurs. We show that there are no instanton solutions to the quantum effective action. The equations for a point classical source of color spin are solved, and we show that the field infrared energy becomes linearly divergent in the limit of spontaneous magnetization. This implies bag formation, and an electric Meissner effect confining the bag contents.     

Hidden constants: The θ parameter of QCD and the cosmological constant of N = 8 supergravity

For field theories that include the abelian gauge field A_μν? the field equations allow an arbitrary integration constant, which does not appear in the lagrangian but which does affect the physics. We present two applications: (i) the θ parameter of effective lagrangians for chiral symmetry breaking in QCD, and (ii) the cosmological constant in N = 8 supergravity, which does not require a gauging of the O(8) symmetry, but is rather due to a spontaneous breakdown of supersymmetry.     

Precocious scaling and nonperturbative effects in QCD

The onset of nonperturbative effects in QCD is studied in two ways: (1) by means of the nonvanishing vacuum expectation value of 〈g ² F ²〉 introduced by Shifman, Vainshtein and Zakharov; (2) using a finite energy sum rule (FESR) for the renormalization group function β. Our considerations are based upon the recently proposed “physical” β_MMOM, which is gauge invariant and shows explicit mass-decoupling.     

Reformulation of general relativity as a gauge theory

The starting point is a spinor affine space-time. At each point, two-component spinors and a basis in spinor space, called “spin frame,” are introduced. Spinor affine connections are assumed to exist, but their values need not be known. A metric tensor is not introduced. Global and local gauge transformations of spin frames are defined with GL(2) as the gauge group. Gauge potentials B_μ are introduced and corresponding fields F_μν are defined in analogy with the Yang-Mills case. Gravitational field equations are derived from an action principle. Incases of physical interest SL(2, C) is taken as the gauge group, instead of GL(2). In the special case of metric space-times the theory is identical with general relativity in the Newman-Penrose formalism. Linear combinations of B_μ are generalized spin coefficients, and linear combinations of F_μν are generalized Weyl and Ricci tensors and Ricci scalar. The present approach is compared with other formulations of gravitation as a gauge field.     

Einstein–Maxwell gravity with additional corrections

Motivated by the E ₈×E ₈ heterotic string theory, we obtain topological black hole solutions of Einstein–Maxwell gravity with additional corrections. We consider the Gauss–Bonnet (GB) and (F _μν F ^μν )² terms as an effective quartic order Lagrangian of gauge–gravity coupling and investigate geometric and thermodynamic properties of the black hole solutions. We also analyze the effects of the GB term as well as the correction of Maxwell field on the properties of the solutions.     

Interacting instantons, 1N expansion and the gluon condensate

Based on the dilute gas approximation (DGA) with repulsive and dipole interactions we discuss the N dependence of the vacuum energy density, 〈α_SF_μν^aF_μν^a〉 and of the topological charge correlation function at the crossover point of the instanton driven β function with the strong coupling one.     

The problem of confinement: From two to four dimensions

The Coulomb law of “electrodynamics” in two space time dimensions in extended to four dimensions. The result is that antisymmetric tensor potentials A_μν? subject to the gauge transformation δA_μν? = ?_μΛ_ν? + ?_?Λ_?μ + ?_?Λ_μν can be effectively used as confining potentials.     

First-order equations for gauge fields in spaces of dimension greater than four

We consider the possibility of satisfying the gauge field equations in dimensions greater than four by imposing linear relations amongst the components of the field strength tensor, F_μν, generalising the idea of self-duality in four dimensions.     

On the geometrical aspects of electromagnetism,I

The trajectory of a charged test particle under a Lorentz force is obtained as the geodesic of a riemannian four dimensional manifold. Originally, the geodesic equation is nonlinear in some vector field A′_μ. The nonlinearity is traded in for the correct characteristic $\text{e}\text{m}$ of the test particle through a gauge condition, imposed upon A′_μ, which turns the geodesic into the fully covariant linear and gauge invariant Lorentz equation. Fitting the $\text{e}\text{m}$ ratio inside the gauge leaves F′_μν independent of $\text{e}\text{m}$ and allows its identification with the E.-M. tensor F_μν. This four dimensional approach allows the identification of the fifth coordinate used in Kaluza's geometrization |1,2|. The gauge function appears as the sum of Hamilton-Jacobi function plus an additional term, related to the “length” of the trajectory. It is this latter term which guarantees the correct “normalisation” of the $\text{e}\text{m}$ ratio.     

Non-transversality of the Yang-Mills self-energy in the planar gauge

It is shown that the Yang-Mills self-energy in the planar gauge is non-transverse, even though this self-energy satisfies the appropriate Ward identity. The non-transversality implies that the one-loop counterterm is no longer proportional to (F_μν^a)².     

Cosmological solutions with Calabi-Yau compactification

Assuming a Calabi-Yau compactification, cosmological solutions are presented in ten-dimensional, N=1 Yang-Mills supergravity theory with the curvature squared term (R²_μνϱσ −4R_μν² + R²). In a vacuum state, Kasner-type soluti ons exist as well as (four-dimensional Minkoswki space-time)×(a Calabi-Yau space). In the later stage of the universe the (four-dimensional Friedmann universe)×(a constant Calabi-Yau space) is realized asymptotically like an attractor. This solution is asymptotically stable against small perturbations.     

The axial anomaly and anti-symmetric tensor fields

Spin-$\text{1}\text{2}$ fermions are coupled to external axial vector and rank-2 anti-symmetic tensor fields. The chiral U(1) Ward identity is shown to have anomalous structure given by $\text{F}{}_{\mathrm{\mu \nu }}\text{F}\text{?}{}^{\mathrm{\mu \nu }}$ only with F_μν the axial vector field strength tensor. No Additional axial anomalied are introduced due to the presence of the anti-symmetric tensor fields.     

String-like topological excitations of the electromagnetic field

In order to analyze the topological properties of an arbitrary configuration of the electromagnetic field, its strength F_μν is expressed in terms of new auxiliary fields which replace the gauge potential A_μ. These new fields have only physical singularities even in the presence of monopoles (no Dirac strings) and exhibit a new local O(1, 1) symmetry which replaces the gauge invariance. Boundary conditions on these fields may induce localized string-like singularities or topological defects which act as sources of magnetic field. A typical defect which emerges is a sort of tadpole formed by a non-quantized monopole attached to one or more magnetic strings of finite length. For topological reasons the total magnetic charge is quantized.     

Properties of quark matter governed by quantum chromodynamics (II). Renormalization schemes in quark matter

Renormalization schemes are examined (in the Coulomb gauge) for quantum chromodynamics in the presence of quark matter. We demand that the effective coupling constant for all schemes become congruent with the vacuum QCD running coupling constant as the matter chemical potential, μ, goes to zero. Also, to enable us to standardize with the vacuum QCD running coupling constant at some asymptotic momentum transfer, $\text{|}\text{p}{}_0\text{|,}\text{we keep}\text{μ ? ¦}\text{p}{}_0\text{¦}$, to ensure that the matter contribution is negligible at this point. This means all schemes merge with vacuum QCD at $\text{|}\text{p}{}_0\text{|}$ and beyond. Two renormalization group invariants are shown to emerge: (i) the effective or invariant charge, g_inv², which is, however, scheme dependent and (ii) g²(M)/S(M), where S(M)^?1 is the Coulomb propagator, which is scheme independent. The only scheme in which g_inv² is scheme independent and identical to g²(M)/S(M) is the screened charged scheme (previous paper) characterised by the normalization of the entire Green function, S^?1, to unity. We conclude that this is the scheme to be used if one wants to identify with the experimental effective coupling in perturbation theory. However, if we do not restrict to perturbation theory all schemes should be allowed. Although we discuss matter QCD in the Coulomb gauge, the above considerations are quite general to gauge theories in the presence of matter.     

Quantum inequivalence of different field representations

The gauge theories of antisymmetric tensor potentials A_μν and A_μν? describe 1 and 0 degrees of freedom, respectively. Yet we show the gravitational trace anomalies of A_μν and a scalar field A to be different, and that of A_μν? to be non-vanishing. Corresponding inequivalences also occur in their one-loop counterterms when the spacetime has non-trivial topology. Furthermore, the coupling of A_μν? to gravity provides a gauge principle derivation of the cosmological constant. Possible applications to supergravity are also discussed.     

Constraints on the behaviour of the e+e− hadron annihilation cross section in asymptotically free theories and in theories with anomalous dimensions

A new approach is proposed to the problem of the relationship between the e⁺e^? hadron annihilation cross section and the behaviour of the hadronic vacuum polarization tensor Π_μν(q) in the space-like region. By using this approach based on the principles of functional analysis, one can uniquely transform the information about the behaviour of Π_μν(q) at q² → ?∞, which is available in asymptotically free theories and in theories with anomalous dimensions, into constraints on the e⁺e^? total cross section.