Asymptotic behaviour of multiple scattering on infinite number of parallel demi-planes

The exact solution for the scattering of electromagnetic waves on an infinite number of parallel demi-planes has been obtained by J.F. Carlson and A.E. Heins in 1947 using the Wiener-Hopf method. We analyze their solution in the semiclassical limit of small wavelength and find the asymptotic behaviour of the reflection and transmission coefficients. The results are compared with the ones obtained within the Kirchhoff approximation

Strings in Yang-Mills-Higgs theory coupled to gravity

Non-Abelian strings for an Einstein-Yang-Mills-Higgs theory are explicitly constructed. We consider N_f Higgs fields in the fundamental representation of the U(1)xSU(N_c) gauge group in order to have a color-flavor SU(N_c) group remaining unbroken. Choosing a suitable ansatz for the metric, Bogomol'nyi-like first order equations are found and rotationally symmetric solutions are proposed. In the N_f = N_c case, solutions are local strings and are shown to be truly non-Abelian by parameterizing them in terms of orientational collective coordinates. When N_f > N_c, the solutions correspond to semilocal strings which, beside the orientational degrees of freedom, acquire additional collective coordinates parameterizing their transverse size. The low-energy effective theories for the correspondent moduli are found, showing that all zero modes are normalizable in presence of gravity, even in the semilocal case.Comment: 20 pages, no figure, modified version with new title, abstract and an additional section completing the study of effective theories. Physical Review D in pres

Composite non-Abelian Flux Tubes in N=2 SQCD

Composite non-Abelian vortices in N=2 supersymmetric U(2) SQCD are investigated. The internal moduli space of an elementary non-Abelian vortex is CP^1. In this paper we find a composite state of two coincident non-Abelian vortices explicitly solving the first order BPS equations. Topology of the internal moduli space T is determined in terms of a discrete quotient CP^2/Z_2. The spectrum of physical strings and confined monopoles is discussed. This gives indirect information about the sigma model with target space T.Comment: 37 pages, 7 figures, v3 details added, v4 erratum adde

Non-Abelian Semilocal Strings in N=2 Supersymmetric QCD

We consider a benchmark bulk theory in four-dimensions: N=2 supersymmetric QCD with the gauge group U(N) and N_f flavors of fundamental matter hypermultiplets (quarks). The nature of the BPS strings in this benchmark theory crucially depends on N_f. If N_f\geq N and all quark masses are equal, it supports non-Abelian BPS strings which have internal (orientational) moduli. If N_f>N these strings become semilocal, developing additional moduli \rho related to (unlimited) variations of their transverse size. Using the U(2) gauge group with N_f=3,4 as an example, we derive an effective low-energy theory on the (two-dimensional) string world sheet. Our derivation is field-theoretic, direct and explicit: we first analyze the Bogomol'nyi equations for string-geometry solitons, suggest an ansatz and solve it at large \rho. Then we use this solution to obtain the world-sheet theory. In the semiclassical limit our result confirms the Hanany-Tong conjecture, which rests on brane-based arguments, that the world-sheet theory is N=2 supersymmetric U(1) gauge theory with N positively and N_e=N_f-N negatively charged matter multiplets and the Fayet-Iliopoulos term determined by the four-dimensional coupling constant. We conclude that the Higgs branch of this model is not lifted by quantum effects. As a result, such strings cannot confine. Our analysis of infrared effects, not seen in the Hanany-Tong consideration, shows that, in fact, the derivative expansion can make sense only provided the theory under consideration is regularized in the infrared, e.g. by the quark mass differences. The world-sheet action discussed in this paper becomes a bona fide low-energy effective action only if \Delta m_{AB}\neq 0.Comment: 36 pages, no figure

Geodesic motion in the space-time of cosmic strings interacting via magnetic fields

We study the geodesic motion of test particles in the space-time of two Abelian-Higgs strings interacting via their magnetic fields. These bound states of cosmic strings constitute a field theoretical realization of p-q-strings which are predicted by inflationary models rooted in String Theory, e.g. brane inflation. In contrast to previously studied models describing p-q-strings our model possesses a Bogomolnyi-Prasad-Sommerfield (BPS) limit. If cosmic strings exist it would be exciting to detect them by direct observation. We propose that this can be done by the observation of test particle motion in the space-time of these objects. In order to be able to make predictions we have to solve the field equations describing the configuration as well as the geodesic equation numerically. The geodesics can then be classified according to the test particle's energy, angular momentum and momentum along the string axis. We find that the interaction of two Abelian-Higgs strings can lead to the existence of bound orbits that would be absent without the interaction. We also discuss the minimal and maximal radius of orbits and comment on possible applications in the context of gravitational wave emission.Comment: v1: 22 pages including 17 figures; v2: new figure added, section on observables added; acccepted for publication in Phys. Rev.

Domain Lines as Fractional Strings

We consider N=2 supersymmetric quantum electrodynamics (SQED) with 2 flavors, the Fayet--Iliopoulos parameter, and a mass term $\beta$ which breaks the extended supersymmetry down to N=1. The bulk theory has two vacua; at $\beta=0$ the BPS-saturated domain wall interpolating between them has a moduli space parameterized by a U(1) phase $\sigma$ which can be promoted to a scalar field in the effective low-energy theory on the wall world-volume. At small nonvanishing $\beta$ this field gets a sine-Gordon potential. As a result, only two discrete degenerate BPS domain walls survive. We find an explicit solitonic solution for domain lines -- string-like objects living on the surface of the domain wall which separate wall I from wall II. The domain line is seen as a BPS kink in the world-volume effective theory. We expect that the wall with the domain line on it saturates both the $\{1,0\}$ and the $\{{1/2},{1/2}\}$b central charges of the bulk theory. The domain line carries the magnetic flux which is exactly 1/2 of the flux carried by the flux tube living in the bulk on each side of the wall. Thus, the domain lines on the wall confine charges living on the wall, resembling Polyakov's three-dimensional confinement.Comment: 28 pages, 13 figure, v2 typos fixed and reference adde

The effect of dark strings on semilocal strings

Dark strings have recently been suggested to exist in new models of dark matter that explain the excessive electronic production in the galaxy. We study the interaction of these dark strings with semilocal strings which are solutions of the bosonic sector of the Standard Model in the limit $\sin^2\theta_{\rm w}=1$, where $\theta_{\rm w}$ is the Weinberg angle. While embedded Abelian-Higgs strings exist for generic values of the coupling constants, we show that semilocal solutions with non-vanishing condensate inside the string core exist only above a critical value of the Higgs to gauge boson mass ratio when interacting with dark strings. Above this critical value, which is greater than unity, the energy per unit length of the semilocal-dark string solutions is always smaller than that of the embedded Abelian-Higgs-dark string solutions and we show that Abelian-Higgs-dark strings become unstable above this critical value. Different from the non-interacting case, we would thus expect semilocal strings to be stable for values of the Higgs to gauge boson mass ratio larger than unity. Moreover, the one-parameter family of solutions present in the non-interacting case ceases to exist when semilocal strings interact with dark strings.Comment: 16 pages including 6 figures; stability analysis adde

Thermodynamics of Vortices in the Plane

The thermodynamics of vortices in the critically coupled abelian Higgs model, defined on the plane, are investigated by placing $N$ vortices in a region of the plane with periodic boundary conditions: a torus. It is noted that the moduli space for $N$ vortices, which is the same as that of $N$ indistinguishable points on a torus, fibrates into a $CP_{N-1}$ bundle over the Jacobi manifold of the torus. The volume of the moduli space is a product of the area of the base of this bundle and the volume of the fibre. These two values are determined by considering two 2-surfaces in the bundle corresponding to a rigid motion of a vortex configuration, and a motion around a fixed centre of mass. The partition function for the vortices is proportional to the volume of the moduli space, and the equation of state for the vortices is $P(A-4\pi N)=NT$ in the thermodynamic limit, where $P$ is the pressure, $A$ the area of the region of the plane occupied by the vortices, and $T$ the temperature. There is no phase transition.Comment: 17 pages, DAMTP 93-3

Perturbation approach to multifractal dimensions for certain critical random matrix ensembles

Fractal dimensions of eigenfunctions for various critical random matrix ensembles are investigated in perturbation series in the regimes of strong and weak multifractality. In both regimes we obtain expressions similar to those of the critical banded random matrix ensemble extensively discussed in the literature. For certain ensembles, the leading-order term for weak multifractality can be calculated within standard perturbation theory. For other models such a direct approach requires modifications which are briefly discussed. Our analytical formulas are in good agreement with numerical calculations.Comment: 28 pages, 7 figure

Pipelike current-carrying vortices in two-component condensates

We study straight vortices with global longitudinal currents in the Bogomol'ny limit of the Abelian Higgs model with two charged scalar fields. The model possesses global SU(2) and local electromagnetic U(1) symmetries spontaneously broken to global U(1) group, and corresponds to a semilocal limit of the standard electroweak model. We show that the contribution of the global SU(2) current to the vortex energy is proportional to the total current squared. Locally, these vortices carry also longitudinal electromagnetic currents, while the total electromagnetic current flowing through a transverse section of the vortex is always zero. The vortices with high winding numbers have, in general, a nested pipelike structure. The magnetic field of the vortex is concentrated at a certain distance from the geometric center of the vortex, thus resembling a "pipe." This magnetic pipe is layered between two electrically charged pipes that carry longitudinal electric currents in opposite directions.Comment: 11 pages, 14 figures, RevTeX 4.1; v2: references added, minor changes, Figure 8 (a visualization of the nested structure of the pipelike vortex) is replaced, published versio