Search

The electroweak monopole, when coupled to gravity, turns to the Reissner-Nordstrom type primordial magnetic blackhole whose mass is bounded below, with the lower bound $M_P \sqrt \alpha$. This changes the overall picture of the monopole production mechanism in the early universe drastically and has deep implications in cosmolpgy. In particular, this enhances the possibility that the electroweak monopoles turned to the primordial magnetic blackholes could become the seed of stellar objects and galaxies, and account for the dark matter of the universe. Moreover, this tells that we have a new type of primordial blackhole different from the popular primordial blackhole in cosmology, the electroweak primordial magnetic blackhole based on a totally different production mechanism. We discuss the physical implications of the electroweak primordial magnetic blackhole.

One of the urgent issues in high energy physics is the experimental confirmation of the electroweak monopole predicted by the standard model, and currently MoEDAL at LHC is actively searching for the monopole. However, the present LHC cannot produce the monopole if the mass is bigger than 7 TeV, while the monopole mass is expected to be around $M_W/\alpha \simeq 11~\text{TeV}$. In this paper we discuss how LHC could circumbent this energy constraint and produce the monopole even when the mass is bigger than 7 TeV, based on the following ideas. First, in the topological production of the monopole the baby monopole mass at creation could be considerably smaller than the adolescent mass. Second, the binding energy of the monopole-antimonopole pair could effectively reduce the mass of the bound state. We discuss how these ideas can actually be realized at LHC to produce the monopole pairs. In particular, we argue that LHC could produce the baby electroweak monopoles whose mass could be around 5.3 TeV, smaller than the adolescent monopole mass around 11.0 TeV. Moreover, we show that LHC could produce the monopolium bound state with mass around 2.5 TeV, even when the total mass of the monopole-antimonopole pair is around 10.6 TeV. Our analysis could play an important role for MoEDAL experiment.

We report on a search for magnetic monopoles (MMs) produced in ultraperipheral Pb--Pb collisions during Run-1 of the LHC. The beam pipe surrounding the interaction region of the CMS experiment was exposed to 184.07 \textmu b$^{-1}$ of Pb--Pb collisions at 2.76 TeV center-of-mass energy per collision in December 2011, before being removed in 2013. It was scanned by the MoEDAL experiment using a SQUID magnetometer to search for trapped MMs. No MM signal was observed. The two distinctive features of this search are the use of a trapping volume very close to the collision point and ultra-high magnetic fields generated during the heavy-ion run that could produce MMs via the Schwinger effect. These two advantages allowed setting the first reliable, world-leading mass limits on MMs with high magnetic charge. In particular, the established limits are the strongest available in the range between 2 and 45 Dirac units, excluding MMs with masses of up to 80 GeV at 95\% confidence level., Comment: As accepted by PRL. 7 pages, 4 figures

The Abelian decomposition of QCD tells that there are two types of gluons in QCD, the color neutral neurons and colored chromons, which behave differently. This strongly implies that QCD has two types of gluon jets, the neuron jet and chromon jet. One quarter of the gluon jets is made of the neuron jets which have sharper jet radius and smaller particle multiplicity, while three quarters of them are made of chromon jets which have the broader jet radius and larger particle multiplicity. Moreover, the neuron jet has a distinct color flow which forms an ideal color dipole pattern, while the chromon jets have distorted dipole pattern. In this paper we provide five circumferential evidences of the existence of two types of gluon jets from the existing ALEPH and DELPHI data on $e \bar e \rightarrow Z \rightarrow b \bar b g$ decay and the CMS data on Pb-Pb heavy ion collision.

We propose the ultra high energy cosmic ray recently detected by Telescope Array to be the electroweak monopole, and present theoretical arguments which support this. This strongly motivates the necessity for the ``cosmic" MoEDAL experiment which could back up our proposal. To confirm this we propose Telescope Array to measure the magnetic charge of the ultra high energy cosmic ray particles with SQUID.

The Abelian decomposition of QCD tells that there are two types of gluons, the color neutral neurons and colored chromons. We propose to confirm the Abelian decomposition testing the existence of two types of gluon jets experimentally. We predict that one quarter of the gluon jet is made of the neurons which has the color factor 3/4 and the sharpest jet radius and smallest charged particle multiplicity, while the three quarters of the gluon jet are made of the chromons with the color factor 9/4 which have the broadest jet radious (broader than the quark jet). Moreover, we argue that the neuron jet has a distinct color flow which forms an ideal color dipole, while the quark and chromon jets have distorted dipole pattern. To test the plausibility of this proposal we suggest to analyse the gluon distribution against the jet shape (the sphericity) and/or particle multiplicity from the existing gluon jet events and look for two distinct peaks in the distribution., Comment: arXiv admin note: substantial text overlap with arXiv:1812.11300

We propose an effective theory of non-Abelian superconductivity, an SU(2)xU(1) extension of the Abelian Landau-Ginzburg theory, which could be viewed as an effective theory of ferromagnetic superconductivity made of spin-up and spin-down doublet Cooper pair. Just like the Abelian Landau-Ginzburg theory it has the U(1) electromagnetic interaction, but the new ingredient is the non-Abelian SU(2) gauge interaction between the spin doublet Cooper pair. A remarkable feature of the theory is the mixing between the photon and the diagonal part of the SU(2) gauge boson. After the mixing it has massless gauge boson (the massless non-Abelian spinon) and massive gauge boson (the massive photon), in addition to the massive off-diagonal gauge bosons (the massive non-Abelian spinons) which induces the spin-flip interaction between the spin up and down components of the Cooper pair. So, unlike the ordinary Landau-Ginzburg theory it has a long range interaction mediated by the massless non-Abelian spinon, which could be responsible for the long range magnetic order and spin waves observed in ferromagnetic superconductors. The theory is characterized by three scales. In addition to the correlation length fixed by the mass of the Higgs field it has two different penetration lengths, the one fixed by the mass of the photon (which generates the well known Meissner effect) and the other fixed by the mass of the off-diagonal spinons (which determines the scale of the spin flip interaction). The non-Abelian structure of the theory naturally accommodates new topological objects, the non-Abrikosov quantized spin vortex (as well as the well known Abrikosov vortex) and non-Abelian spin monopole. We discuss the physical implications of the non-Abelian Landau-Ginzburg theory., Comment: 12 pages, 2 figures

A search for highly electrically charged objects (HECOs) and magnetic monopoles is presented using 2.2 fb-1 of p - p collision data taken at a centre of mass energy (ECM) of 8 TeV by the MoEDAL detector during LHC's Run-1. The data were collected using MoEDAL's prototype Nuclear Track Detector array and the Trapping Detector array. The results are interpreted in terms of Drell-Yan pair production of stable HECO and monopole pairs with three spin hypotheses (0, 1/2 and 1). The search provides constraints on the direct production of magnetic monopoles carrying one to four Dirac magnetic charges (4gD) and with mass limits ranging from 590 GeV/c^2 to 1 TeV/c^2. Additionally, mass limits are placed on HECOs with charge in the range 10e to 180e, where e is the charge of an electron, for masses between 30 GeV/c^2 and 1 TeV/c^2.

Schwinger showed that electrically-charged particles can be produced in a strong electric field by quantum tunnelling through the Coulomb barrier. By electromagnetic duality, if magnetic monopoles (MMs) exist, they would be produced by the same mechanism in a sufficiently strong magnetic field. Unique advantages of the Schwinger mechanism are that its rate can be calculated using semiclassical techniques without relying on perturbation theory, and the finite MM size and strong MM-photon coupling are expected to enhance their production. Pb-Pb heavy-ion collisions at the LHC produce the strongest known magnetic fields in the current Universe, and this article presents the first search for MM production by the Schwinger mechanism. It was conducted by the MoEDAL experiment during the 5.02 TeV/nucleon heavy-ion run at the LHC in November 2018, during which the MoEDAL trapping detectors (MMTs) were exposed to 0.235 nb$^{-1}$ of Pb-Pb collisions. The MMTs were scanned for the presence of magnetic charge using a SQUID magnetometer. MMs with Dirac charges 1$g_D$ $\leq$ $g$ $\leq$ 3$g_D$ and masses up to 75 GeV/c$^2$ were excluded by the analysis. This provides the first lower mass limit for finite-size MMs from a collider search and significantly extends previous mass bounds., Comment: Minor fixes to the authorship list found during production

We discuss the Abelian and non-Abelian monopoles which could exist in condensed matters. We show how the Dirac monopole can be regularized by the charge screening, and argue that the Dirac monopole of mass of hundred meVs could exist in dielectric condensed matters. Moreover, we generalize this result to non-Abelian condensed matters to show the existence of the non-Abelian monopole configuration in two-gap condensed matters, and present explicit monopole solutions.

The MoEDAL trapping detector, consists of approximately 800 kg of aluminium volumes. It was exposed during Run-2 of the LHC program to 6.46 fb^-1 of 13 TeV proton-proton collisions at the LHCb interaction point. Evidence for dyons (particles with electric and magnetic charge) captured in the trapping detector was sought by passing the aluminium volumes comprising the detector through a SQUID magnetometer. The presence of a trapped dyon would be signalled by a persistent current induced in the SQUID magnetometer. On the basis of a Drell-Yan production model, we exclude dyons with a magnetic charge ranging up to 5 Dirac charges, and an electric charge up to 200 times the fundamental electric charge for mass limits in the range 790 - 3130 GeV., Comment: arXiv admin note: text overlap with arXiv:1903.08491

We show that the electroweak monopole can be regularized with a non-vacuum electromagnetic permittivity. This allows us to set a new BPS bound for the monopole mass, which implies that the mass may not be smaller than 2.98 TeV, more probably 3.75 TeV. We demonstrate that the same method can also regularize the Dirac monopole, which enhances the possibility to construct the Dirac monopole of mass of a few hundred meV in condensed matters. We discuss the physical implications of our result.

MoEDAL is designed to identify new physics in the form of stable or pseudostable highly ionizing particles produced in high-energy Large Hadron Collider (LHC) collisions. Here we update our previous search for magnetic monopoles in Run 2 using the full trapping detector with almost four times more material and almost twice more integrated luminosity. For the first time at the LHC, the data were interpreted in terms of photon-fusion monopole direct production in addition to the Drell-Yan-like mechanism. The MoEDAL trapping detector, consisting of 794 kg of aluminum samples installed in the forward and lateral regions, was exposed to 4.0 fb$^{-1}$ of 13 TeV proton-proton collisions at the LHCb interaction point and analyzed by searching for induced persistent currents after passage through a superconducting magnetometer. Magnetic charges equal to or above the Dirac charge are excluded in all samples. Monopole spins 0, 1/2 and 1 are considered and both velocity-independent and -dependent couplings are assumed. This search provides the best current laboratory constraints for monopoles with magnetic charges ranging from two to five times the Dirac charge., Comment: 7 pages REVTeX 4, 11 figures, 1 table, matches published version in Physical Review Letters

We propose a simple way to test the Abelian decomposition of QCD, the existence of two types of gluons, experimentally at LHC. The Abelian decomposition decomposes the gluons to the color neutral neurons and colored chromons gauge independently. This refines the Feynman diagram in a way that the color conservation is explicit, and generalizes the quark model to the quark and chromon model. We predict that the neuron jet has the color factor 3/4 and has a sharpest jet radius and smallest particle multiplicity, while the chromon jet with the color factor 9/4 remains the broadest jet. Moreover, the neuron jet has a distinct color flow which forms an ideal color dipole, while the quark and chromon jets have distorted dipole pattern.

We show how to calculate the effective potential of SU(3) QCD which tells that the true minimum is given by the monopole condensation. To do this we make the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. In the perturbative regime this decomposes the Feynman diagram in such a way that the conservation of color is explicit. Moreover, this shows the existence of two gluon jets, the neuron jet and chromon jet, which can be verified by experiment. In the non-perturbative regime, the decomposition puts QCD to the background field formalism and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry, and provides us an ideal platform to calculate the one-loop effective action of QCD. Integrating out the chromons from the Weyl symmetric Abelian decomposition of QCD gauge invariantly imposing the color reflection invariance, we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result, in particular the possible existence of the vacuum fluctuation mode of the monopole condensation in QCD., Comment: arXiv admin note: text overlap with arXiv:1606.02374

After Dirac introduced the monopole, topological objects have played increasingly important roles in physics. In this review we discuss the role of the knot, the most sophisticated topological object in physics, and related topological objects in various areas in physics. In particular, we discuss how the knots appear in Maxwell's theory, Skyrme theory, and multi-component condensed matter physics., Comment: arXiv admin note: substantial text overlap with arXiv:1704.05975

Recently it has been pointed out that the skyrmions carry two independent topology, the baryon topology and the monopole topology. We provide more evidence to support this. In specific, we prove that the baryon number $B$ can be decomposed to the monopole number $m$ and the shell number $n$, so that $B$ is given by $B=mn$. This tells that the skyrmions may more conveniently be classified by two integers $(m,n)$. This is because the rational map which determines the baryon number in the popular multi-skyrmion solutions actually describes the monopole topology $\pi_2(S^2)$ which is different from the baryon topology $\pi_3(S^3)$. Moreover, we show that the baby skyrmions can also be generalized to have two topology, $\pi_1(S^1)$ and $\pi_2(S^2)$, and thus should be classified by two topological numbers $(m,n)$. Furthermore, we show that the vacuum of the Skyrme theory can be classified by two topological numbers $(p,q)$, the $\pi_1(S^1)$ of the sigma-field and the $\pi_3(S^2)$ of the normalized pion-field. This means that the Skyrme theory has multiple vacua similar to the Sine-Gordon theory and QCD combined together. This puts the Skyrme theory in a totally new perspective. We discussthe physical implications of our results.

We discuss the cosmological production and the successive evolution of the electroweak (Cho-Maison) monopole in the standard model, and estimate the remnant monopole density at present universe. We confirm that, although the electroweak phase transition is of the first order, it is very mildly the first order. So the monopole production comes from the thermal fluctuations of the Higgs field after the phase transition, not the vacuum bubble collisions during the phase transition. Moreover, while the monopoles are produced copiously around the Ginzburg temperature $T_G\simeq 59.6~{\rm TeV}$, most of them are annihilated as soon as created. This annihilation process continues very long time, untill the monopoles are decoupled from the other matters when the temperature cools to about 30 MeV. As the result the remnant monopole density at present universe becomes very small, of $10^{-11}$ of the critical density, too small to affect the standard cosmology and too small be the dark matter. We discuss the physical implications of our results on the ongoing monopole detection experiments, in particular on MoEDAL, IceCube, ANTARES, Auger, and Super-Kamiokande.

The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons (the neurons) and the colored valence gluons (the chromons) gauge independently naturally generalizes the quark model to the quark and chromon model which could play the central role in hadron spectroscopy. We discuss the color reflection symmetry, the fundamental symmetry of the quark and chromon model, and explain how it describes the glueballs and the glueball-quarkonium mixing in QCD. We present the numerical analysis of glueball-quarkonium mixing in $0^{++}$, $2^{++}$, and $0^{-+}$ sectors below 2 GeV, and show that in the $0^{++}$ sector $f_0(500)$ and $f_0(1500)$, in the $2^{++}$ sector $f_2(1950)$, and in the $0^{-+}$ sector $\eta(1405)$ and $\eta(1475)$ could be identified as predominantly the glueball states. We discuss the physical implications of our result., Comment: arXiv admin note: text overlap with arXiv:1503.08890

We present the multiply phased current carrying vortex solutions in the U(1) gauge theory coupled to an $(N+1)$-component SU(N+1) scalar multiplet in the Bogomolny limit. Our vortex solutions correspond to the static vortex dressed with traveling waves along the axis of symmetry. What is notable in our vortex solutions is that the frequencies of traveling waves in each component of the scalar field can have different values. The energy of the static vortex is proportional to the topological charge of $CP^N$ model in the BPS limit, and the multiple phase of the vortex supplies additional energy contribution which is proportional to the Noether charge associated to the remaining symmetry.

We present a family of gravitationally coupled electroweak monopole solutions in Einstein-Weinberg-Salam theory. Our result confirms the existence of globally regular gravitating electroweak monopole which changes to the magnetically charged black hole as the Higgs vacuum value approaches to the Planck scale. Moreover, our solutions could provide a more accurate description of the monopole stars and magnetically charged black holes.

We continue our investigation of quark confinement using a particular variant of the Cho-Duan-Ge gauge independent Abelian decomposition. The decomposition splits the gauge field into a restricted Abelian part and a coloured part in a way that preserves gauge covariance. The restricted part of the gauge field can be divided into a Maxwell term and a topological term. Previously, we showed that by a particular choice of this decomposition we could fully describe the confining potential using only the restricted gauge field. We proposed that various topological objects (a form of magnetic monopole) could arise in the restricted field which would drive confinement. Our mechanism does not explicitly refer to a dual Meissner effect, nor does it use centre vortices. We did not need to gauge fix or introduce any new dynamical fields. We show that if we do gauge fix as well as performing the Abelian decomposition then it is possible to ensure that the topological part of the restricted field fully accounts for the confining potential. Our relationship is exact: there is no approximation or model involved. This isolates the objects responsible for confinement from non-confining contributions to the gauge field, allowing a direct search for our proposed topological objects. Using numerical studies in SU(2), we confirm that our proposed monopoles are present in the field, and the winding number associated with these monopoles is a key factor driving quark confinement. In SU(2), our monopoles are described by two parameters. We show that it is possible to re-parametrise the Yang Mills action and the functional integration measure in terms of these variables (plus the necessary additional parameters). We can thus treat the monopoles as dynamical variables in the functional integral. This might be the first step in a future analytical computation to complement our numerical results., Comment: 35 pages, 13 figures. arXiv admin note: text overlap with arXiv:1503.07033

Based on the observation that the skyrmion in Skyrme theory can be viewed as a dressed monopole, we show that the skyrmions have two independent topology, the baryon topology $\pi_3(S^3)$ and the monopole topology $\pi_2(S^2)$. With this we propose to classify the skyrmions by two topological numbers $(m,n)$, the monopole number $m$ and the shell (radial) number $n$. In this scheme the popular (non spherically symmetric) skyrmions are classified as the $(m,1)$ skyrmions but the spherically symmetric skyrmions are classified as the $(1,n)$ skyrmions, and the baryon number $B$ is given by $B=mn$. Moreover, we show that the vacuum of the Skyrme theory has the structure of the vacuum of the Sine-Gordon theory and QCD combined together, which can also be classified by two topological numbers $(p,q)$. This puts the Skyrme theory in a totally new perspective., Comment: 8 pages, 4 figures

The Abelian decomposition of QCD which decomposes the gluons to the color neutral binding gluons and the colored valence gluons shows that QCD can be viewed as the restricted QCD (RCD) made of the binding gluons which has the valence gluons as colored source, and simplifies the QCD dynamics greatly. In particular, it tells that the gauge covariant valence gluons can be treated as the constituents of hadrons, and generalizes the quark model to the quark and valence gluon model. So it provides a comprehensive picture of glueballs and their mixing with quarkoniums, and predicts new hybrid hadrons made of quarks and valence gluons. We discuss how these predictions could be confirmed experimentally. In particular we present a systematic search for the ground state glueballs and their mixing with quarkoniums below 2 GeV in $0^{++}$, $2^{++}$, and $0^{-+}$ channels within the framework of QCD, and predict the relative branching ratios of the radiative decay of $\psi$ to the physical states.

We investigate the relationship between colour confinement and the gauge independent Cho-Duan-Ge Abelian decomposition. The decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This establishes an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. We circumvent path ordering without needing an additional path integral. By using Stokes' theorem, we can compute the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by certain structures, which occur when one of the quantities parametrising the colour field $n$ winds itself around a non-analyticity in the colour field. If they exist, these structures will lead to a area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and compare the electric and magnetic fields with the patterns expected theoretically. We find that the restricted field strength is dominated by objects which may be peaks a single lattice spacing in size or extended string-like lines of electromagnetic flux. The objects are not isolated monopoles, as they generate electric fields in addition to magnetic fields, and the fields are not spherically symmetric, but may be either caused by a monopole/anti-monopole condensate, some other types of topological objects or a combination of these. Removing these peaks removes the area law scaling of the string tension, suggesting that they are responsible for confinement., Comment: 67 pages, 19 figures

The superradiance phenomena of massive bosons and fermions in the Kerr spacetime are studied in the Bargmann-Wigner formulation. In case of bi-spinor, the four independent components spinors correspond to the four bosonic freedom: one scalar and three vectors uniquely. The consistent description of the Bargmann-Wigner equations between fermions and bosons shows that the superradiance of the type with positive energy $(0<\omega)$ and negative momentum near horizon $(p_{\rm H}<0)$ is shown not to occur. On the other hand, the superradiance of the type with negative energy $(\omega<0)$ and positive momentum near horizon $(0

We show how to generalize the previous result of the monopole condensation in SU(2) QCD to SU(3) QCD. We present the gauge independent Weyl symmetric Abelian decomposition of the SU(3) QCD which decomposes the gluons to the color neutral neurons and the colored chromons. The decomposition allows us to separate the gauge invariant and parity conserving monopole background gauge independently, and reduces the non-Abelian gauge symmetry to a discrete color reflection symmetry which is easier to handle. With this we obtain the infra-red finite and gauge invariant integral expression of the one-loop effective action which is Weyl symmetric in three SU(2) subgroups. Integrating it gauge invariantly imposing the color reflection invariance we obtain the SU(3) QCD effective potential which generates the stable monopole condensation and the mass gap. We discuss the physical implications of our result., Comment: arXiv admin note: substantial text overlap with arXiv:1206.6936 Withdraw for the new and updated file

We maintain that the search for the electroweak monopole is a key issue in the advancement of our understanding of the standard model. Unlike the Dirac monopole in electrodynamics, which is optional, the electroweak monopole should exist within the framework of the standard model. The mass of the electroweak monopole is estimated to be 5 to 7 TeV, but could be as large as 15 TeV. Above threshold its production rate at the LHC is expected to be relatively large, (1/alpha(em)2) times bigger than that of W+W- pairs. The search for the electroweak monopole is one of the prime motivations of the newest LHC experiment, MoEDAL, which is due to start data taking in 2015., Comment: 6 pages, 5 figures

We investigate the relationship between colour confinement and topological structures derived from the gauge invariant Abelian (Cho-Duan-Ge) decomposition. This Abelian decomposition is made imposing an isometry on a colour field $n$ which selects the Abelian direction; the principle novelty of our study is that we have defined this field in terms of the eigenvectors of the Wilson Loop. This allows us to establish an equivalence between the path ordered integral of the non-Abelian gauge fields with an integral over an Abelian restricted gauge field which is tractable both theoretically and numerically in lattice QCD. By using Stokes' theorem, we can relate the Wilson Loop in terms of a surface integral over a restricted field strength, and show that the restricted field strength may be dominated by topological structures, which occur when one of the parameters parametrising the colour field $n$ winds itself around a non-analyticity in the colour field. If they exist, these objects will lead to an area law scaling for the Wilson Loop and provide a mechanism for quark confinement. We search for these structures in quenched lattice QCD. We perform the Abelian decomposition, and find that the restricted field strength is dominated by peaks on the lattice. Wilson Loops containing these peaks show a stronger area-Law and thus provide the dominant contribution to the string tension., Comment: 8 pages, 3 figures; v2 some minor changes (including updated numerical results), accepted for publication in Physics Letters

The recent MoEDAL experiment at LHC to detect the electroweak monopole makes the theoretical prediction of the monopole mass an urgent issue. We discuss different ways to estimate the mass of the electroweak monopole. We first present a scaling argument which indicates that the mass of the electroweak monopole to be around 4 TeV. To justify this we construct finite energy analytic dyon solutions which could be viewed as the regularized Cho-Maison dyon, modifying the coupling strengths of the electromagnetic interaction of $W$-boson in the standard model. Our result demonstrates that a genuine electroweak monopole whose mass scale is much smaller than the grand unification scale can exist, which can actually be detected at the present LHC., Comment: arXiv admin note: substantial text overlap with arXiv:hep-th/0210299, arXiv:hep-th/9707038

We present finite energy analytic monopole and dyon solutions whose size is fixed by the electroweak scale. Our result shows that genuine electroweak monopole whose mass is around 6.7 TeV could exist, which could be detected at LHC., Comment: 4 pages, 2 figures. arXiv admin note: substantial text overlap with arXiv:hep-th/9705213

We investigate the relationship between colour confinement and the monopoles derived from the Cho-Duan-Ge decomposition. These monopoles, unlike Dirac and 't Hooft monopoles, do not require a singular gauge field and are defined for any choice of gauge (and are not just restricted to, for example, the maximum Abelian gauge). The Abelian decomposition is defined in terms of a colour field $n$; the principle novelty of our study is that we have used a unique definition of this field in terms of the eigenvectors of the Wilson Loop. This allows us to investigate the relationship between the gauge invariant monopoles and confinement both analytically and numerically, as well as retaining the maximal possible symmetry within the colour field so that it is able to see all the monopoles in an SU($N_C$) calculation. We describe how the Abelian decomposition is related to the Wilson Loop, so that the string tension may be calculated from the field strength related to the decomposed (or restricted) Abelian field. We discuss the structures in the colour field which may cause an area law in the Wilson Loop, which turn out to be magnetic monopoles. If these monopoles are present, they will lead to an area law scaling of the Wilson Loop and thus be at least partially responsible for confinement. We search for these monopoles in quenched lattice QCD. We show that the string tension is dominated by peaks in the restricted field strength, at least some of which are located close to structures in the colour field consistent with with theoretical expectations for the monopoles. We show that the string tension extracted from the monopole contribution to the restricted field is close to that of the entire original field; again suggesting that confinement can at least partially be explained in terms of these monopoles., Comment: Lattice 2012 (Chiral Symmetry), 7 pages

We compare two competing conjectures of the color confinement in QCD, the monopole condensation and the Abelian dominance, and show that it is the monopole condensation which is responsible for the confinement. To demonstrate this we present a new gauge invariant integral expression of the one-loop QCD effective action which has no infra-red divergence. With this we show that, just as the GSO-projection restores the supersymmetry and modular invariance in NSR string theory, the color reflection invariance ("the C-projection") assures the gauge invariance and the stability of the monopole condensation. This establishes the monopole dominance in QCD. In doing so we point out critical defects in the calculation of the Savvidy-Nielsen-Olesen (SNO) effective action.

We consider Weyl symmetric structure of the classical vacuum in quantum chromodynamics. In the framework of formalism of gauge invariant Abelian projection we show that classical vacuums can be constructed in terms of Killing vector fields on the group SU(3). Consequently, homotopic classes of Killing vector fields determine the topological structure of the vacuum. In particular, the second homotopy group \pi_2(SU(3)/U(1)\times U(1)) describes all topologically non-equivalent vacuums which are classified by two topological numbers. For each given Killing vector field one can construct six vacuums forming Weyl sextet representation. An interesting feature of SU(3) gauge theory is that it admits a Weyl symmetric vacuum represented by a linear superposition of the six vacuums from the Weyl vacuum sextet. A non-trivial manifestation of Weyl symmetry is demonstrated on monopole solutions. We construct a family of finite energy monopole solutions in Yang-Mills-Higgs theory which includes Weyl monopole sextet. From the analysis of the classical vacuum structure and monopole solutions we conjecture that a similar Weyl symmetric vacuum structure can be realized in quantum theory., Comment: 13 pages

Viewing Einstein's theory as the gauge theory of Lorentz group, we construct the most general vacuum connections which have vanishing curvature tensor and show that the vacuum space-time can be classified by the knot topology $\pi_3(S^3)\simeq \pi_3(S^2)$ of $\pi_3(SO(3,1))$. With this we obtain the gauge independent vacuum decomposition of Einstein's theory to the vacuum and gauge covariant physical parts. We discuss the physical implications of our result in quantum gravity.

Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the gravitational connection (the gauge potential of Lorentz group) $\vGm_\mu$ into the restricted connection made of the potential of the maximal Abelian subgroup $H$ of Lorentz group $G$ and the valence connection made of $G/H$ part of the potential which transforms covariantly under Lorentz gauge transformation. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, the light-like (or null) decomposition and the non light-like (or non-null) decomposition, because Lorentz group has two maximal Abelian subgroups. In this decomposition the role of the metric $g_\mn$ is replaced by a four-index metric tensor $\vg_\mn$ which transforms covariantly under the Lorentz group, and the metric-compatibility condition $\nabla_\alpha g_\mn=0$ of the connection is replaced by the gauge and generally covariant condition ${\mathscr D}_\mu \vg^\mn=0$. The decomposition shows the existence of a restricted theory of gravitation which has the full general invariance but is much simpler and has less physical degrees of freedom than Einstein's theory. Moreover, it tells that the restricted gravity can be written as an Abelian gauge theory, which implies that the graviton can be described by a massless spin-one field.

~Based on the gauge invariant quark canonical momentum we construct two theoretically possible decompositions of nucleon momentum to those of quarks and gluons. We predict that either 6% or 21% of nucleon momentum is carried by gluons, depending on what type of gluons are in nucleons. We clarify the existing confusions on this problem and discuss the physical implications of our result on the proton spin crisis problem.

We discuss the shortfalls of existing resolutions of the long-standing gauge invariance problem of the canonical decomposition of the nucleon spin to the spin and angular momentum of quarks and gluons. We provide two logically flawless expressions of nucleon spin which have different physical meanings, using the gauge independent Abelian decomposition. The first one is based on the assumption that all gluons (binding and valence gluons) contribute to the nucleon spin, but the second one is based on the assumption that only the binding gluons (and the quarks) contribute to it. We propose the second expression to be the physically correct one.

Topologically non-trivial vacuum structure in gravity models with Cartan variables (vielbein and contortion) is considered. We study the possibility of vacuum space-time tunneling in Einstein gravity assuming that the vielbein may play a fundamental role in quantum gravitational phenomena. It has been shown that in the case of RP3 space topology the tunneling between non-trivial topological vacuums can be realized by means of Eguchi-Hanson gravitational instanton. In Riemann-Cartan geometric approach to quantum gravity the vacuum tunneling can be provided by means of contortion quantum fluctuations. We define double self-duality condition for the contortion and give explicit self-dual configurations which can contribute to vacuum tunneling amplitude., Comment: 11 pages, 1 fig. is added, final version

A new Lorentz gauge gravity model with R^2-type Lagrangian is proposed. In the absence of classical torsion the model admits a topological phase with an arbitrary metric. We analyze the equations of motion in constant curvature space-time background using the Lagrange formalism and demonstrate that the model possesses a minimal set of dynamic degrees of freedom for the torsion. Surprisingly, the number of torsion dynamic degrees of freedom equals the number of physical degrees of freedom for the metric tensor. An interesting feature of the model is that the spin two mode of torsion becomes dynamical essentially due to the non-linear structure of the theory. We perform covariant one-loop quantization of the model for a special case of constant curvature space-time background. We treat the contortion as a quantum field variable whereas the metric tensor is kept as a classical object. We discuss a possible mechanism of an emergent Einstein gravity as a part of the effective theory induced due to quantum dynamics of torsion., Comment: 16 pages, final version

Assuming that the dilaton is the dark matter of the universe, we propose an experiment to detect the relic dilaton using the electromagnetic resonant cavity, based on the dilaton-photon conversion in strong electromagnetic background. We calculate the density of the relic dilaton, and estimate the dilaton mass for which the dilaton becomes the dark matter of the universe. With this we calculate the dilaton detection power in the resonant cavity, and compare it with the axion detection power in similar resonant cavity experiment., Comment: 23 pages, 2 figures

Based on the fact that the scalar curvature of the internal space determines the mass of the dilaton in higher-dimensional unified theories, we show how the dilaton mass can explain the origin of mass and resolve the hierarchy problem. Moreover, we show that cosmology puts a strong constraint on dilaton mass, and requires the scale of the internal space to be larger than $10^{-9} m$., Comment: 5 pages, 1 figure

We present a topological classification of vacuum space-time. Assuming the 3-dimensional space allows a global chart, we show that the static vacuum space-time of Einstein's theory can be classified by the knot topology $\pi_3(S^3)=\pi_3(S^2)$. Viewing Einstein's theory as a gauge theory of Lorentz group and identifying the gravitational connection as the gauge potential of Lorentz group, we construct all possible vacuum gravitational connections which give a vanishing curvature tensor. With this we show that the vacuum connection has the knot topology, the same topology which describes the multiple vacua of SU(2) gauge theory. We discuss the physical implications of our result in quantum gravity., Comment: 4 pages

We propose a reformulation of general relativity by making the Abelian decomposition of Einstein's theory. Based on the view that Einstein's theory can be interpreted as a gauge theory of Lorentz group, we decompose the Einstein's gravitational connection (the gauge potential of Lorentz group $\vGm_\mu$) into the restricted connection made of the potential of the maximal Abelian subgroup $H$ of Lorentz group $G$ and the valence connection made of $G/H$ part of the potential which transforms covariantly under Lorentz group. With this decomposition we show that the Einstein's theory can be decomposed into the restricted part made of the restricted connection which has the full Lorentz gauge invariance and the valence part made of the valence connection which plays the role of gravitational source of the restricted gravity. We show that there are two different Abelian decomposition of Einstein's theory, because Lorentz group has two maximal Abelian subgroups. In this decomposition the role of the space-time metric $g_\mn$ is replaced by a four-index metric tensor $\vg_\mn$ which transforms covariantly under the Lorentz group, and the metric-compatibility condition $\nabla_\alpha g_\mn=0$ of the connection is replaced by the gauge covariant condition $D_\mu \vg^\mn$ which tells that $\vg_\mn$ is invariant under the parallel transport along the $\pro_\mu$-direction defined by $\vGm_\mu$. We discuss the physical implications of the Abelian decomposition. In particular, we argue that the decomposition implies the existence of a restricted theory of gravitation which has the full general invariance but has less physical degrees of freedom., Comment: 19 pages, minor corrections

We consider one-loop effective action of SU(3) QCD with a most general constant chromomagnetic (chromoelectric) background which has two independent Abelian field components. The effective potential with a pure magnetic background has a local minimum only when two Abelian components H_{\mu\nu}^3 and H_{\mu\nu}^8 of color magnetic field are orthogonal to each other. The non-trivial structure of the effective action has important implication in estimating quark-gluon production rate and p_T-distribution in quark-gluon plasma. In general the production rate depends on three independent Casimir invariants, in particular, it depends on the relative orientation between chromoelectric fields., Comment: 6 pages, 3 figures (9 pages in published version)

We discuss the quantization of the restricted gauge theory of SU(2) QCD regarding it as a second-class constraint system, and construct the BRST symmetry of the constrained system in the framework of the improved Dirac quantization scheme. Our analysis tells that one could quantize the restricted QCD as if it is a first-class constraint system., Comment: 18 pages

The effects of light propagation in constant magnetic and electric backgrounds are considered in the framework of the effective action approach. We use the exact analytic series representation for the one-loop effective action of QED and apply it to the birefringence effect. Analytical results for the light velocity modes are obtained for weak and strong field regime. We present asymptotic formulae for the light velocity modes for the ultra strong magnetic field which can be realized in some neutron stars., Comment: 9 pages, 4 figs, accepted by Phys. Rev. D

We discuss topological objects, in particular the non-Abrikosov vortex and the magnetic knot made of the twisted non-Abrikosov vortex, in two-gap superconductor. We show that there are two types of non-Abrikosov vortex in Ginzburg-Landau theory of two-gap superconductor, the D-type which has no concentration of the condensate at the core and the N-type which has a non-trivial profile of the condensate at the core, under a wide class of realistic interaction potential. Furthermore, we show that we can construct a stable magnetic knot by twisting the non-Abrikosov vortex and connecting two periodic ends together, whose knot topology $\pi_3(S^2)$ is described by the Chern-Simon index of the electromagnetic potential. We discuss how these topological objects can be constructed in $\rm MgB_2$ or in liquid metallic hydrogen., Comment: 20 pages, 12 figures

We present a simple method to calculate the one-loop effective action of QCD which reduces the calculation to that of SU(2) QCD. For the chromomagnetic background we show that the effective potential has an absolute minimum only when two color magnetic fields $H_{\mu\nu}^3$ and $H_{\mu\nu}^8$ are orthogonal to each other. For the chromoelectric background we find that the imaginary part of the effective action has a negative signature, which implies the gluon pair-annihilation. We discuss the physical implications of our result., Comment: 4 pages, 2 figures

Motivated by the instability of the Savvidy-Nielsen-Olesen (SNO) vacuum we make a systematic search for a stable magnetic background in pure SU(2) QCD. It is shown that Wu-Yang monopole-antimonopole pair is unstable under vacuum fluctuations. However, it is shown that a pair of axially symmetric monopole-antimonopole string configuration is stable, provided the distance between the two strings is small enough (less than a critical value). The existence of a stable monopole-antimonopole string background strongly supports that a magnetic condensation of monopole-antimonopole pairs can indeed generate a dynamical symmetry breaking, and thus a desired magnetic confinement of color, in QCD.