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.     

Gluon condensate from SU(2) lattice gauge theory

Recent Monte Carlo results are analyzed in terms of an operator product expansion for Wilson loops of small size. The value of 〈α_sG_μν^aG_μν^a〉 is found to be consistent with previous phenomenological estimates.     

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.     

A field configuration closer to the true QCD vacuum

An effective action for QCD at one-loop order, which is real, manifestly Lorentz and gauge invariant and which depends on an infinite family of gauge invariants (tr(F _μν F _μν), tr(F _μν F _μν F _?σ F _?σ),...), is obtained. Moreover, anAnsatz for a vacuum configuration is made, whose corresponding vacuum energy density is lower than the one for the SavvidyAnsatz. Both the cases of pure QCD and of QCD with massless fermions are considered.     

The electromagnetic string with spin

The relations betweeb a field F_μν^M satisfying the usual Maxwell equations and a field F_μν^D satisfying the symmetric Maxwell-Dirac equations, and the singular potential solving both of these is given. The action principle is formulated in both forms and the reality of the string is shown. A string with spin is constructed by placing electric charges at its end-points. The motion and interactions of the string, the relation between flux and angular momentum quantization and the passage to two-body Hamiltonians are examined.     

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.     

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.     

Vacuum condensates in supersymmetric gluodynamics

We analyse the restrictions imposed by supersymmetric Ward identities on the dimension-six condensates in supersymmetric gluodynamics. It is shown that the system of the Ward identities admits a nonzero value for the four-fermion condensate \(\left\langle {\left( {\lambda \sigma _\mu T^a \bar \lambda } \right)^2 } \right\rangle _0 \) while 〈f ^abc F _μν ^a F _νρ ^b F _ρμ ^c 〉₀ must vanish.     

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.     

Effects of Eu3+  Fe3+ exchange interaction on the spin Hamiltonian parameters of Fe3+ in EuGaG

The anisotropic exchange $\text{1}\text{3}\text{a}{}_{\mathrm{\mu \nu }}\text{Y}{}_{\mathrm{\mu \nu }}\text{(L}{}_{\mathrm{<mtext>Eu</mtext>}}\text{)S}{}_{\mathrm{<mtext>Eu</mtext>}}\text{· S}{}_{\mathrm{<mtext>Fe</mtext>}}\text{(0 < μ ? 6)}$ is incorporated with the isotropic exchange ?2 a₀₀S_Eu · S_Fe to interpret the observed spin-Hamiltonian parameters g and D of Fe³⁺ doped into EuGaG. Calculations from the observed g shifts yield a value of a₀₀ equal to 0.01 K. In order to explain the observed D shift, it is concluded that the spherical harmonics Y_μν(L_Eu) with μ > 2 are of dominant importance.     

p‐wave superconductors in dilaton gravity

In this paper, we study peculiar properties of p‐wave superconductors in dilaton gravity. The scale invariance of the bulk geometry is effectively broken due to the existence of a dilaton. By coupling the dilaton to the non‐Abelian gauge field, i.e., ‐1/4 e^{‐β Φ} F^a_μνF^aμν, we find that the dissipative conductivity of the normal phase decreases and approaches zero at the zero frequency as β increases. Intuitively, the system behaves more and more like an insulator. When the hairy solution is turned on, the system crosses a critical point to the superconducting phase. We find that the critical chemical potential decreases with the increasing of β and the maximum height of the conductivity is suppressed gradually which are consistent with our intuition for insulator/supercondutor transition.     

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.     

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.     

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.     

Messung der Hyperfeinstrukturaufspaltung des4F9/2-Grundzustandes im Co59-I-Spektrum und Bestimmung des Quadrupolmomentes des Co59-Kernes

The hyperfine structure splittings of the electronic ground statea ⁴ F _9/2 in the Co⁵⁹-I-spectrum have been measured with a magnetic atomic-beam resonance-apparatus. From these splittings the magnetic dipole and electric quadrupole interaction constants are found to beA (a ⁴ F _/2)=(450,284±0,01) Mc/sec,B (a ⁴ F _9/2)= (139,63±0,5) Mc/sec. Taking into account the mixture of thea ⁴ F _9/2 state with states of the same 3d ⁷ 4s ²-electron-configuration, an electric quadrupole moment of Co⁵⁹ ofQ=(0,404±0,04) 10^?24 cm² was obtained. No Sternheimer-correction has been included.     

ESR study of Fe3+ and Mn2+ ions on trigonal sites in ilmenite structure MgTiO3

Electron spin resonance has been observed for Fe³⁺ and Mn²⁺ ions occupying sites with trigonal symmetry in undoped and doped Verneuil-grown crystals of the ilmenite type compound MgTiO₃. At 300 K, the fine structure parameters in the spin Hamiltonian are (in 10^?4cm^?1) D = +844 (± 1), (a? F) = +118 (± 1), a = 69 (± 7) for Fe³⁺ and D = +164 (± 1), (a ? F) = +10.2 (± l), a = 7.0 (± 1) for Mn²⁺. These values are compared with literature data for Fe³⁺ and Mn²⁺ in other oxides, especially Al₂o₃, with particular reference to the recent “superposition” theory of the effect of a trigonal distortion. From the orientation of the axes of cubic pseudosymmetry of the spin Hamiltonian, and with the assumption that a has the same sign for both ions, it is proposed that Fe³⁺ and Mn²⁺ occupy the same octahedral site, namely the Mg²⁺ site. Anomalous line splittings observed for one sample were attributed to twinning on (0001) or {1120} planes.     

Gluon condensate and the interquark potential

We construct a potential for qurkonium systems using as the basic ingredients the gluon condensate, i.e., 〈0∥G_μν^aG_μν^a∥0〉 ≠ 0 to incorporate nonperturbative effects and using quark screening. The potential is able to account satisfactorily for the s$\text{s}$, c$\text{c}$ and b$\text{b}$ bound states with a flavor independent, essentially constant value for the effective coupling constant $\text{(}\text{α}{}_{\mathrm{<mtext>S</mtext>}}\text{≈ 0.45)}$. We also investigate heavier quark systems with the constant $\text{α}{}_{\mathrm{S}}$ and find that for quark mass ? 20 GeV the potential is essentially coulombic.     

The ideal relativistic rotating gas as a perfect fluid with spin

We show that the ideal relativistic spinning gas at complete thermodynamical equilibrium is a fluid with a non-vanishing spin density tensor σ_μν. After having obtained the expression of the local spin-dependent phase-space density f(x, p)_στ in the Boltzmann approximation, we derive the spin density tensor and show that it is proportional to the acceleration tensor Ω_μν constructed with the Frenet-Serret tetrad. We recover the proper generalization of the fundamental thermodynamical relation, involving an additional term −(1/2)Ω_μνσ^μν. We also show that the spin density tensor has a non-vanishing projection onto the four-velocity field, i.e. t^μ = σ_μνu^ν ≠ 0, in contrast to the common assumption t^μ = 0, known as Frenkel condition, in the thus-far proposed theories of relativistic fluids with spin. We briefly address the viewpoint of the accelerated observer and inertial spin effects.     

Anomaly cancelling terms from the elliptic genus

We calculate the heterotic string one-loop diagram in 2n + 2 dimensions with one external B_μν and n external gravitons and/or gauge bosons. The result is a modular integral over the weight zero terms of the character valued partition function (or elliptic genus) of the theory, and can be directly expressed in terms of the factor which multiplies TrF² − TrR² in the field theory anomaly. The integrands have a non-trivial dependence on the modular parameter τ, reflecting contributions not only from the physical massless states but also from an infinity of “unphysical” modes. Some of them are identical to integrands which have been discussed recently in relation with Atkin-Lehner symmetry and the cosmological constant. As a corollary we find a method to compute these integrals without using Atkin-Lehner transformations.