Vacuum Symmetry Research Articles

SU(3)family gauge symmetry and the axion

We analyze the structure of a recently proposed effective field theory (EFT) for the generation of quark and lepton mass ratios and mixing angles, based on the spontaneous breaking of an $SU(3)$ family gauge symmetry at a high scale $F$. We classify the Yukawa operators necessary to seed the masses, making use of the continuous global symmetries that they preserve. One global $U(1)$, in addition to baryon number and electroweak hypercharge, remains unbroken after the inclusion of all operators required by standard model fermion phenomenology. An associated vacuum symmetry insures the vanishing of the first-family quark and charged-lepton masses in the absence of the family gauge interaction. If this $U(1)$ symmetry is taken to be exact in the EFT, broken explicitly by only the QCD-induced anomaly, and if the breaking scale $F$ is taken to lie in the range ${10}^{9}--{10}^{12}\text{ }\text{ }\mathrm{GeV}$, then the associated Nambu-Goldstone boson is a potential QCD axion.

General SU(2) L × SU(2) R × U(1) EM Sigma Model with External Sources, Dynamical Breaking and Spontaneous Vacuum Symmetry Breaking

We give a general $SU(2)_L\times SU(2)_R$ $\times U(1)_{EM}$ sigma model with external sources, dynamical breaking and spontaneous vacuum symmetry breaking, and present the general formulation of the model. It is found that $\sigma $ and $\pi ^0$ without electric charges have electromagnetic interaction effects coming from their internal structure. A general Lorentz transformation relative to external sources $J_{gauge}$ $=(J_{A_\mu},J_{A_\mu ^\kappa})$ is derived, using the general Lorentz transformation and the four-dimensional current of nuclear matter of the ground state with $J_{gauge}$ = 0, we give the four-dimensional general relations between the different currents of nuclear matter systems with $J_{gauge}\neq 0$ and those with $J_{gauge}=0$. The relation of the density's coupling with external magnetic field is derived, which conforms well to dense nuclear matter in a strong magnetic field. We show different condensed effects in strong interaction about fermions and antifermions, and give the concrete scalar and pseudoscalar condensed expressions of $\sigma_0$ and $\pi_0$ bosons. About different dynamical breaking and spontaneous vacuum symmetry breaking, the concrete expressions of different mass spectra are obtained in field theory. This paper acquires the running spontaneous vacuum breaking value $\sigma_0^{\prime},$ and obtains the spontaneous vacuum breaking in terms of the running $\sigma_0^{\prime}$, which make nucleon, $\sigma $ and $\pi $ particles gain effective masses. We achieve both the effect of external sources and nonvanishing value of the condensed scalar and pseudoscalar paticles. It is deduced that the masses of nucleons, $\sigma $ and $\pi $ generally depend on different external sources.

Theoretical Study on the Structures and Electronic Spectra of TCNE2−

Investigations into the charge-separated states and electron-transfer transitions in tetracyanoethylene (TCNE) complexes have recently generated much interest. In this work we present theoretical calculations showing that the most stable structure of the dianion TCNE2- has D2d symmetry in vacuum as well as in the solvents dichloromethane and acetonitrile. By means of the coupled cluster linear response, we compute the vertical electronic spectrum in both the gas phase and solution. The theoretical results are compared to the experimental data and good agreement is achieved.

Momentum transfer from vacuum field to anisotropic electromagnetic media

It is demonstrated that many novel vacuum effects will be caused if an anisotropic electromagnetic environment, which can break the universal symmetry of vacuum, is achieved. It is thus possible for the momentum to be transferred from the vacuum zero-point field to the anisotropic electromagnetic media. In addition to the effect considered by Feigel more recently [A. Feigel, Phys. Rev. Lett. 92 (2004) 020404], there may exist another vacuum-fluctuation contribution to the momentum of a medium. Such an effect has a relativistic origin (resulting from the relativistic transformation of the optical constants), which, however, was not taken into account by Feigel.

ON THE DEGENERACIES OF THE MASS-SQUARED DIFFERENCES FOR THREE-NEUTRINO OSCILLATIONS

Using an algebraic formulation, we explore two well-known degeneracies involving the mass-squared differences for three-neutrino oscillations assuming CP symmetry is conserved. For vacuum oscillation, we derive the expression for the mixing angles that permit invariance under the interchange of two mass-squared differences. This symmetry is most easily expressed in terms of an ascending mass order. This can be used to reduce the parameter space by one half in the absence of the MSW effect. For oscillations in matter, we derive within our formalism the known approximate degeneracy between the standard and inverted mass hierarchies in the limit of vanishing θ13. This is done with a mass ordering that permits the map Δ31↦-Δ31. Our techniques allow us to translate mixing angles in this mass order convention into their values for the ascending order convention. Using this dictionary, we demonstrate that the vacuum symmetry and the approximate symmetry invoked for oscillations in matter are distinctly different.

On the elliptic system arising from a self-gravitating Born–Infeld Abelian Higgs theory

We study a system of elliptic equations from the Abelian Born–Infeld system coupled with the Einstein equations under the boundary condition of symmetric vacuum (nontopological type). When the total string number satisfies 1 ⩽ N < 1/4π G, where G is the gravitational constant, we construct a family of solutions to the system. The qualitative properties of the solutions are quite different from the solutions with the boundary condition of broken vacuum symmetry.

Modular origin of chiral diffeomorphisms and their fuzzy analogs in higher-dimensional quantum field theories

The infinite-dimensional conformal symmetries beyond the Moebius-group (the vacuum symmetry) of chiral theories are shown to allow a natural derivation and interpretation in the operator-algebraic modular setting of algebraic QFT. In this way one learns that the diffeomorphisms of the circle beyond the Moebius group are bona fide Wigner symmetries with respect to suitably chosen non-vacuum state vector. The separation of chiral diffeomorphism symmetry from the issue of the structure of the energy–momentum tensor of 2-dimensional conformal theories permits the use of these symmetries in more general chiral theories which one encounters in the algebraic lightfront holography of massive d⩾1+1 dimensional QFTs. They only act locally on the lightfront projection but correspond to a new class of “fuzzy” symmetries in the original theory before the projection. These fuzzy symmetries remained hidden to quantization methods since they have a pure quantum origin; they do not require any spacetime noncommutativity and are in complete harmony with the causality and locality of the real time (non-commutative) operator algebra structure. Their use makes recent attempts to explain the desired universal structure of a possible future quantum Bekenstein-like area law in terms of Virasoro algebra structures on black hole horizons more palatable.

DOES ONE OBSERVE CHIRAL SYMMETRY RESTORATION IN BARYON SPECTRUM?

It has recently been suggested that the parity doublet structure seen in the spectrum of highly excited baryons may be due to effective chiral symmetry restoration for these states. We review the recent developments in this field. We demonstrate with a simple quantum-mechanical example that it is a very natural property of quantum systems that a symmetry breaking effect which is important for the low-lying spectrum of the system, can become unimportant for the highly-lying states; the highly lying states reveal a multiplet structure of nearly degenerate states. Using the well-established concepts of quark–hadron duality, asymptotic freedom in QCD and validity of the operator product expansion in QCD, we show that the spectral densities obtained with the local currents that are connected to each other via chiral transformations, very high in the spectrum must coincide. Hence effects of spontaneous breaking of chiral symmetry in QCD vacuum that are crucially important for the low-lying spectra, become irrelevant for the highly-lying states. Then to the extent that identifiable hadronic resonances still exist in the continuum spectrum at high excitations, this implies that the highly excited hadrons must fall into multiplets associated with the representations of the chiral group. We demonstrate that this is indeed the case for meson spectra in the large Nc limit. All possible parity-chiral multiplets are classified for baryons and it is demonstrated that the existing data on highly excited N and Δ states at masses of 2 GeV and higher is consistent with approximate chiral symmetry restoration. However new experimental studies are needed to achieve any definitive conclusions.

Non-perturbative aspects of dual QCD vacuum and confinement

Utilizing the topological structure of the non-Abelian gauge theories, QCD has been analysed as a dual gauge theory. The dynamical breaking of magnetic symmetry of dual QCD vacuum has been shown to push QCD vacuum in a state of dual superconductivity imparting it the non-perturbative colour confining properties. Analysing the flux tube structure of the magnetically condensed vacuum, the characteristic mass scales and other confinement parameters of dual QCD have been computed which have been used to discuss the nature of the QCD vacuum in view of the running nature of strong coupling constant.

FERMION-SECTOR FRUSTRATED SU(4) AS A PREONIC PRECURSOR OF THE STANDARD MODEL

We give a model for composite quarks and leptons based on the semisimple gauge group SU(4), with the preons in the 10 representation; this choice of gauge gluon and preon multiplets is motivated by the possibility of embedding them in an N=6 supergravity multiplet, with the preons and antipreons both in the 20 of SU(6). Hypercolor singlets are forbidden in the fermionic sector of this theory; we propose that the SU(4) symmetry spontaneously breaks to SU (3)× U (1), with the binding of triality nonzero preons and gluons into composites, and with the formation of a color singlet condensate that breaks the initial Z12 vacuum symmetry to Z6. The spin ½ fermionic composites have the triality structure of a quark–lepton family, and the initial Z12 symmetry implies that there are six massless families, which mix to give three distinct families below the scale of the condensate. The spin 1 triality zero composites of the color triplet SU(4) gluons, when coupled to the condensate and with the color singlet representation of the 10 acting as a doorway state, lead to weak interactions of the fermionic composites through an SU(2) gauge algebra. The initial Z12 symmetry implies that this SU(2) gauge algebra structure is doubled, which in turn permits the corresponding independent gauge bosons to couple to chiral components of the composite fermions. Since the U(1) couples to the 10 representation as B-L, an effective SU (2)L× SU (2)R × U (1)B-L electroweak theory arises at the condensate scale, with all composites having the correct electric charge structure. Assuming a mechanism for forming composite Higgs bosons, the Z12→ Z6 symmetry breaking chain implies that below the condensate scale there can be two sets of discrete chiral Z6 triplets of Higgs doublets, as required by a phenomenological model for the CKM matrix that we have analyzed in detail elsewhere. A renormalization group analysis of the SU(4) model shows that the conversion by binding of one 10 of SU(4) to 12 triplets of SU(3) can give a very large, calculable hierarchy ratio between the SU(4) and the hadronic mass scales.

Hadronic and electromagnetic probes of hot and dense nuclear matter

We review the constraints imposed by the spontaneously broken chiral symmetry of the QCD vacuum on the hadron properties at finite temperature T and baryon density ρ B . A restoration of chiral symmetry is indicated by the dropping of the scalar quark condensate q ̄ q at finite T and ρ B in various approaches. This suggests the hadrons to become approximately massless in hot and dense nuclear matter or the vector and axial vector currents to become equal. In this respect we study the properties of hadrons – as produced in relativistic nucleus–nucleus collisions – by means of a covariant hadronic transport approach where scalar and vector hadron self-energies are taken into account explicitly which are modelled in terms of effective ‘chiral’ Lagrangians. Within this transport approach we investigate the reaction dynamics of relativistic heavy-ion collisions and analyse experimental data on π, η, K +, K −, ρ, ω, φ, p ̄ and charmonium production for proton–nucleus and nucleus–nucleus collisions from SIS to SPS energies (1–200 A GeV). Whereas π, η and to some extent K + mesons are found not to change their properties in the nuclear medium substantially, antiprotons and antikaons do show sizeable attractive self-energies as can be extracted from their experimental abundancies and spectra. The properties of the vector mesons ρ, ω and φ at finite baryon density are investigated by their dileptonic decay; the CERES and HELIOS-3 data at SPS energies are found to be incompatible with a ‘bare’ vector meson mass scenario. Here, a description by ‘dropping’ ρ and ω masses leads to a very good reproduction of the data, however, also approaches based on more conventional hadronic interactions as pion polarizations and meson–nucleon scattering amplitudes are compatible with the present dilepton spectra at SPS energies. Constraints from dilepton studies at BEVALAC/SIS energies are investigated in all decay schemes as well as a variety of further observables that allow to disentangle the different scenarios experimentally. Furthermore, the charmonium production and suppression in proton–nucleus and nucleus–nucleus collisions is investigated within the transport approach in order to probe a possible transition to a quark-gluon plasma (QGP) phase. We finally discuss ‘optimized’ observables for an experimental investigation of the restoration of chiral symmetry and/or the phase transition to a quark-gluon plasma.

ε-EXPANSION IN QUANTUM FIELD THEORY IN CURVED SPACE–TIME

We discuss ε-expansion in curved space–time for asymptotically free and asymptotically nonfree theories. The existence of stable and unstable fixed points is investigated for fϕ4 theory and SU(2) gauge theory. It is shown that ε-expansion maybe compatible with aysmptotic freedom on special solutions of the RG equations in a special ase (supersymmetric theory). Using ε-expansion RG technique, the effective Lagrangian for covariantly constant gauge SU(2) field and effective potential for gauged NJL model are found in (4-ε)-dimensional curved space (in linear curvature approximation). The curvature-induced phase transitions from symmetric phase to asymmetric phase (chromomagnetic vacuum and chiral symmetry broken phase, respectively) are discussed for the above two models.

Measurements of early time radiation asymmetry in vacuum and methane-filledHohlraumswith the reemission ball technique

In a previous paper [Phys. Rev. E 53, 5240 (1996)], we presented experimental results of a technique for measuring time resolved symmetry in vacuum Hohlraums irradiated with the laser beams from the NOVA laser located at Lawrence Livermore National Laboratory. The experimental method involved x-ray imaging a high-$Z$ ball placed in the center of a laser irradiated vacuum Hohlraum. The signal from the high-$Z$ ball was measured along the Hohlraum axis, and compared with calculations. In this paper, using this experimental technique, we present time-dependent reemission measurements and calculations of the drive symmetry in vacuum and methane-filled Hohlraums for a shaped laser pulse. We also present a method for determining the time dependence of the radiation flux from the measured reemission signal ratios, and do a modal analysis to determine the values of the dominant Legendre components.

Monopole Condensation and Colour Confinement

A particularly interesting attempt to understand the structure of the QCD vacuum and color confinement is the dual superconductor mechanism [1,2]. By dual Meissner effect, in the presence of a quark-antiquark pair the chromoelectric field is squeezed into flux tubes and the potential energy rises linearly with the distance producing confinement. The detection on the lattice of linear rising potential [3] and of flux tube configurations [4] has given support to this idea. Direct evidence may come from the study of the symmetry of QCD vacuum. Dual superconductivity is indeed the spontaneous breaking of the U(1) symmetry related to monopole charge conservation. The color deconfining transition occurs between the broken magnetic phase, where magnetic monopoles condense, and the symmetric phase where the vacuum is invariant under the action of U(1) magnetic group. This order-disorder transition can be studied by constructing an operator with non trivial magnetic charge and computing its vacuum expectation value (v.e.v.) [5]. A creation operator for a monopole can be defined and its v.e.v. used as an order parameter. In non abelian gauge theories monopoles can be defined by means of abelian projection [6] in analogy with the ‘t Hooft-Polyakov monopole [7,8] in the Georgi-Glashow model. In case of SU(2) or

Dissipative dynamics in a quantum register

A model for a quantum register dissipatively coupled with a bosonic thermal bath is studied. The register consists of $N$ qubits (i.e. spin ${1/2}$ degrees of freedom), the bath is described by $N_b$ bosonic modes. The register-bath coupling is chosen in such a way that the total number of excitations is conserved. The Hilbert space splits allowing the study of the dynamics separately in each sector. Assuming that the coupling with the bath is the same for all qubits, the excitation sectors have a further decomposition according the irreducible representations of the $su(2)$ spin algebra. The stability against environment-generated noise of the information encoded in a quantum state of the register depends on its $su(2)$ symmetry content. At zero temperature we find that states belonging to the vacuum symmetry sector have for long time vanishing fidelity, whereas each lowest spin vector is decoupled from the bath and therefore is decoherence free. Numerical results are shown in the one-excitation space in the case qubit-dependent bath-system coupling.

Studying invisible axion models at high temperature

AbstractDuring the thermal evolution of the universe, symmetry of the vacuum state in the presence of quantum fields should have changed at various stages. A possible indication of this effect on the DFSZ invisible axion model of the Peccei‐Quinn CP conserving mechanism is presented here. To start with, the background theory of this mechanism in the cosmic evolution has been fully reviewed, as well as the leading cosmological arguments setting limits on the mass and coupling of such a particle. The CP conserving lagrangian of the invisible axion model also includes instanton gauge field configurations. In our opinion, these configurations could behave non trivially while decreasing the temperature as a consequence of the vacuum symmetry modifications. The interplay between symmetry modifications and cosmic evolution may thus lead to yet unclear effects. In fact, the model considered here is really quite a baby version of the real world, so that only preliminary indications and bare consistency arguments have been done from it. Nevertheless, the underlying idea, a possible neutral Higgs fields approximate resonance condition, seems to survive even in more sophisticated models.

Perturbative couplings of vector multiplets in N = 2 heterotic string vacua

We study the low-energy effective Lagrangian of N = 2 heterotic string vacua at the classical and quantum level. The couplings of the vector multiplets are uniquely determined at the tree level, while the loop corrections are severely constrained by the exact discrete symmetries of the string vacuum. We evaluate the general transformation law of the perturbative prepotential and determine its form for the toroidal compactifications of six-dimensional N = 1 supersymmetric vacua.

Reaching for the Top

The uninitiated would have had difficulty explaining the excited crowd of physicists filling Fermilab's auditorium on 26 April—especially since the presenters were careful to disclaim an actual discovery. Yet even though skepticism remained the watchword, the excitement of even the most ardent critics was palpable. The multinational 440‐member Collider Detector Facility group at Fermilab's Tevatron may have glimpsed the top quark—the longsought partner of the bottom quark—at 174±17 GeV. This would make the t quark the heaviest fundamental particle yet seen. Indeed, because the observed mass is so close to the mass at which electroweak unification becomes manifest, many speculate that the top quark may hold the secrets to the primordial breaking of vacuum symmetry that is thought to have given masses to elementary particles.

Quasi-primary fields and associativity of chiral algebras

As a step towards writing down associativity conditions for a general extended conformal algebra, we consider Jacobi's identity for a set of quasi-primary fields. In particular, we show that the identity for the subalgebra of operators which generate symmetries of the vacuum can be written in terms of Racah coefficients for su(2). The associativity condition for the full algebra is obtained in an explicit form by considering crossing symmetry of the four-point functions.

Two-dimensional approximation of QED with allowance for finite temperature

We have generalized the two-dimensional approximation of quantum electrodynamics to the case of a finite temperature under the assumption that γ>T2, m2. We have found the thermal corrections for the Green's functions, polarization and mass operators, and also the vertex function. We have shown that in the low-temperature limit these corrections tend to zero. We have considered the physically interesting case of high temperatures and have obtained the Debye charge-screening radius for an electron gas in the ground state. Our result agrees with the corresponding quantity found from the thermodynamic potential of a degenerate electron gas in a strong magnetic field. For the mass operator, the thermal correction has a negative sign and in the high-temperature limit can completely (in the leading logarithmic approximation) compensate the electron energy shift in a magnetic field. An analogous situation obtains for the vertex function. It should be noted especially that in the general case the thermal contribution does not have a Lorentz-invariant structure, but in the particular considered cases invariance (in the two-dimensional (0, 3) subspace) is restored when T≫m, and this leads ultimately to complete compensation of the vacuum contributions to the QED operators. It is possible that this fact is not fortuitous and is analogous to the well-known effect of restoration of the vacuum symmetry in gauge models at high temperatures noted in [4].