Flux String Research Articles

Regge trajectories for mesons in the holographic dual of large-NcQCD

We discuss Regge trajectories of dynamical mesons in large-N_c QCD, using the supergravity background describing N_c D4-branes compactified on a thermal circle. The flavor degrees of freedom arise from the addition of N_f<<N_c D6 probe branes. Our work provides a string theoretical derivation, via the gauge/string correspondence, of a phenomenological model describing the meson as rotating point-like massive particles connected by a flux string. The massive endpoints induce nonlinearities for the Regge trajectory. For light quarks the Regge trajectories of mesons are essentially linear. For massive quarks our trajectories qualitatively capture the nonlinearity detected in lattice calculations.

The baryon static potential from lattice QCD

Lattice QCD simulations offer the possibility of determining the potential between three static quarks from first principles. We review the status of such simulations, and the relative standing of the two theoretical proposals for the baryonic potential: the Delta law (sum of two-body terms) and the Y law (length of three flux strings joined together at a junction). We also present new results on the leading Luscher-like corrections to the asymptotic linear potential.

Moduli stabilization from magnetic fluxes in type I string theory

We show that type I string theory compactified in four dimensions in the presence of constant internal magnetic fields possesses N = 1 supersymmetric vacua, in which all Kähler class and complex structure closed string moduli are fixed. Furthermore, their values can be made arbitrarily large by a suitable tuning of the quantized magnetic fluxes. We present an explicit example for the toroidal compactification on T 6 and discuss Calabi–Yau generalizations. This mechanism can be complementary to other stabilization methods using closed string fluxes but has the advantage of having an exact string description and thus a validity away from the low-energy supergravity approximation. Moreover, it can be easily implemented in constructions of string models based on intersecting D-branes.

Color superconductivity, BPS Zk strings and monopole confinement in N = 2 and N = 4 super Yang-Mills theories

We review some recent developments on BPS string solutions and monopole confinement in the Higgs (or color) superconducting phase of <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 2 and <IMG SRC="/img/revistas/bjp/v34n4a/caln_mai.gif" > or = 4 super Yang-Mills theories. In particular, the monopole magnetic fluxes are shown to be always integer linear combinations of string fluxes. Moreover, a bound for the threshold length of the string breaking is obtained. When the gauge group SU(N) is broken to Z N, the BPS string tension satisfies the Casimir scaling law. Furthermore, in the SU(3) case the string solutions are such that they allow the formation of a confining system with three monopoles.

Color superconductivity,ZNflux tubes, and monopole confinement in deformedN=2*super Yang-Mills theories

We study the ${Z}_{N}$ flux tubes and monopole confinement in deformed $\mathcal{N}{=2}^{*}$ super Yang-Mills theories. In order to do that we consider an $\mathcal{N}=4$ super Yang-Mills theory with an arbitrary gauge group G and with the addition of some $\mathcal{N}=2,$ $\mathcal{N}=1,$ and $\mathcal{N}=0$ deformation terms. We analyze some possible vacuum solutions and phases of the theory, depending on the deformation terms which are added. In the Coulomb phase for the $\mathcal{N}{=2}^{*}$ theory, G is broken to ${U(1)}^{r}$ and the theory has monopole solutions. Then, by adding some deformation terms, the theory passes to the Higgs or color superconducting phase, in which G is broken to its center ${C}_{G}.$ In this phase we construct the ${Z}_{N}$ flux tubes ansatz and obtain the BPS string tension. We show that the monopole magnetic fluxes are linear integer combinations of the string fluxes and therefore the monopoles can become confined. Then, we obtain a bound for the threshold length of the string breaking. We also show the possible formation of a confining system with three different monopoles for the $\mathrm{SU}(3)$ gauge group. Finally we show that the BPS string tensions of the theory satisfy the Casimir scaling law.

Tachyon tube and supertube

We search for tubular solutions in unstable D3-brane. With critical electric field E=1, solutions representing supertubes, which are supersymmetric bound states of fundamental strings, D0-branes, and a cylindrical D2-brane, are found and shown to exhibit BPS-like property. We also point out that boosting such a {\it tachyon tube} solution generates string flux winding around the tube, resulting in helical electric fluxes on the D2-brane. We also discuss issues related to fundamental string, absence of magnetic monopole, and finally more tachyon tubes with noncritical electric field.

Zkstring fluxes and monopole confinement in non-Abelian theories

Recently (hep-th/0104171) we considered N=2 super Yang-Mills with a N=2 mass breakingn term and showed the existence of BPS Z_{k}-string solutions for arbitrary simple gauge groups which are spontaneously broken to non-Abelian residual gauge groups. We also calculated their string tensions exactly. In doing so, we have considered in particular the hypermultiplet in the same representation as the one of a diquark condensate. In the present work we analyze some of the different phases of the theory and find that the magnetic fluxes of the monopoles are multiple of the fundamental Z_{k}-string flux, allowing for monopole confinement in one of the phase transitions of the theory. We also calculate the threshold length for a string breaking. Some of these confining theories can be obtained by adding a N=0 deformation term to N=2 or N=4 superconformal theories.

Flux line lattice structure and behavior in antiphase boundary free vicinal YBa2Cu3O7−δ thin films

Field angle dependent critical current, magneto-optical microscopy and high resolution electron microscopy studies have been performed on YBa2Cu3O7−δ thin films grown on miscut substrates. High resolution electron microscopy images show that the films studied exhibited clean epitaxial growth with a low density of antiphase boundaries and stacking faults. Any antiphase boundaries (APBs) formed near the film substrate interface rapidly healed rather than extending through the thickness of the film. Unlike vicinal films grown on annealed substrates, which contain a high density of antiphase boundaries, magneto-optical imaging showed no filamentary flux penetration in the films studied. The flux penetration is, however, asymmetric. This is associated with intrinsic pinning of flux strings by the tilted a–b planes and the dependence of the pinning force on the angle between the local field and the a–b planes. Field angle dependent critical current measurements exhibited the striking vortex channeling effect previously reported in vicinal films. By combining the results of three complementary characterization techniques it is shown that extended APB free films exhibit markedly different critical current behavior compared to APB rich films. This is attributed to the role of APB sites as strong pinning centers for Josephson string vortices between the a–b planes.

Massive (3+1)-dimensional Aharonov-Bohm fermions in an MIT cylinder

We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 3+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the Hamiltonian. The external sector is also studied and unambiguous results for the Casimir energy of massive fermions in the whole space are obtained.

Dimensional reduction, magnetic flux strings, and domain walls

We study some consequences of dimensionally reducing systems with massless fermions and Abelian gauge fields from 3+1 to 2+1 dimensions. We first consider fermions in the presence of an external Abelian gauge field. In the reduced theory, obtained by compactifying one of the coordinates `a la Kaluza-Klein, magnetic flux strings are mapped into domain wall defects. Fermionic zero modes, localized around the flux strings of the 3+1 dimensional theory, become also zero modes in the reduced theory, via the Callan and Harvey mechanism, and are concentrated around the domain wall defects. We also study a dynamical model: massless $QED_4$, with fermions confined to a plane, deriving the effective action that describes the `planar' system.

Harmonic oscillator interacting with conical singularities

We study the quantum dynamics of a particle interacting harmonically with conical singularities that physically correspond to either a cosmic string, a global monopole, a magnetic flux string or a screw dislocation, by solving the corresponding Schr?dinger equations. Exact expressions for the energy eigenfunctions and eigenvalues are found.

Confinement on the brane

A non-perturbative confinement mechanism has been proposed to explain the fate of the unbroken gauge group on the world-volume of annihilating D-brane-anti-D-brane pairs. In this paper, we examine this phenomenon closely from several different perspectives. Existence of the confinement mechanism is most easily seen by noticing that the fundamental string emerges as the confined electric flux string at the end of the annihilation process. After reviewing the confinement proposal in general, this is shown explicitly in the D2-anti-D2 case in the M-theory limit. Finally, we address the crucial issue of whether and how confinement occurs in the weakly coupled limit of string theory.

Casimir energy of massive MIT fermions in an Aharonov-Bohm background

We study the effect of a background flux string on the vacuum energy of massive Dirac fermions in 2+1 dimensions confined to a finite spatial region through MIT boundary conditions. We treat two admissible self-adjoint extensions of the Hamiltonian and compare the results. In particular, for one of these extensions, the Casimir energy turns out to be discontinuous at integer values of the flux.

DIRAC FIELDS IN THE BACKGROUND OF A MAGNETIC FLUX STRING AND SPECTRAL BOUNDARY CONDITIONS

We study the problem of a Dirac field in the background of an Aharonov–Bohm flux string. We exclude the origin by imposing spectral boundary conditions at a finite radius then shrinked to zero. Thus, we obtain a behavior of the eigenfunctions which is compatible with the self-adjointness of the radial Hamiltonian and the invariance under integer translations of the reduced flux. After confining the theory to a finite region, we check the consistency with the index theorem, and evaluate its vacuum fermionic number and Casimir energy.

Membranes from five-branes and fundamental strings from D p-branes

We argue that the M2-brane is realized as a topological soliton on a coincident pair of M5-and anti-M5-branes, as the two five-branes annihilate each other. The topology and quantum numbers of this world-volume soliton are discussed in some detail, and its formation is explained qualitatively. It follows from a compactification that a D4-anti-D4 pair annihilate and produce type II fundamental strings. The phenomenon is best described as the confinement of a world-volume U(1) gauge field on D4-anti-D4, where the confined electric flux string is identified as the fundamental string. This generalizes to other D p-anti-D p systems, and solves a puzzle recently pointed out by Witten.

Field theoretic branes and tachyons of the QCD string

Dvali and Shifman have proposed a field-theoretic mechanism for localizing gauge fields to “branes” in higher dimensional spaces using confinement in a bulk gauge theory. The resulting objects have a number of qualitative features in common with string theory D-branes; they support a gauge field and flux strings can end on them. In this letter, we explore this analogy further, by considering what happens when N of these “branes” approach each other. Unlike in the case of D-branes, we find a reduction of the gauge symmetry as the “branes” overlap. This can be attributed to a tachyonic instability of the flux string stretching between the branes.

Quantum and string shape fluctuations in the dual monopole Nambu–Jona–Lasinio model with dual Dirac strings

The magnetic monopole condensate is calculated in the dual Monopole Nambu–Jona–Lasinio model with dual Dirac strings suggested in [1,2] as a functional of the dual Dirac string shape. The calculation is carried out in the tree approximation in the scalar monopole–antimonopole collective excitation field. The integration over quantum fluctuations of the dual–vector monopole–antimonopole collective excitation field around the Abrikosov flux line and string shape fluctuations are performed explicitly. We claim that there are important contributions of quantum and string shape fluctuations to the magnetic monopole condensate.

Evolution of a non-Abelian cosmic string network

We describe a numerical simulation of the evolution of an S3 cosmic string network which takes fully into account the noncommutative nature of the cosmic string fluxes and the topological obstructions which hinder strings from moving past each other or intercommuting. The influence of initial conditions, string tensions, and other parameters on the network’s evolution is explored. Contrary to some previous suggestions, we find no strong evidence of the “freezing” required for a string-dominated cosmological scenario. Instead, the results in a broad range of regimes are consistent with the familiar scaling law, i.e., a constant number of strings per horizon volume. The size of this number, however, can vary quite a bit, as can other overall features. There is a surprisingly strong dependence on the statistical properties of the initial conditions. We also observe a rich variety of interesting new structures, such as light string webs stretched between heavier strings, which are not seen in Abelian networks.

Erratum: Baryon magnetic moments and proton spin: A model with collective quark rotation [Phys. Rev.D 55, 2644 (1997)

We analyse the baryon magnetic moments in a model that relates them to the parton spins $\Delta u$, $\Delta d$, $\Delta s$, and includes a contribution from orbital angular momentum. The specific assumption is the existence of a 3-quark correlation (such as a flux string) that rotates with angular momentum $\langle L_z \rangle$ around the proton spin axis. A fit to the baryon magnetic moments, constrained by the measured values of the axial vector coupling constants $a^{(3)}=F+D$, $a^{(8)}=3F-D$, yields $\langle S_z \rangle = 0.08 \pm 0.13$, $\langle L_z \rangle = 0.39 \pm 0.09$, where the error is a theoretical estimate. A second fit, under slightly different assumptions, gives $\langle L_z \rangle = 0.37 \pm 0.09$, with no constraint on $\langle S_z \rangle$. The model provides a consistent description of axial vector couplings, magnetic moments and the quark polarization $\langle S_z \rangle$ measured in deep inelastic scattering. The fits suggest that a significant part of the angular momentum of the proton may reside in a collective rotation of the constituent quarks.

Flux string in quantum billiards with two particles

We examine the quantum motion of two particles, one heavier than the other, confined in a rectangular domain in two and three dimensions, which interact through a contact force. We show that the system is reduced to a one-particle Aharonov-Bohm billiard with the presence of a closed flux string.