Confinement and Localization on Domain Walls

We continue the studies of localization of the U(1) gauge fields on domain walls. Depending on dynamics of the bulk theory the gauge field localized on the domain wall can be either in the Coulomb phase or squeezed into flux tubes implying (Abelian) confinement of probe charges on the wall along the wall surface. First, we consider a simple toy model with one flavor in the bulk at weak coupling (a minimal model) realizing the latter scenario. We then suggest a model presenting an extension of the Seiberg--Witten theory which is at strong coupling, but all theoretical constructions are under full control if we base our analysis on a dual effective action. Finally, we compare our findings with the wall in a "nonminimal" theory with two distinct quark flavors that had been studied previously. In this case the U(1) gauge field trapped on the wall is exactly massless because it is the Goldstone boson of a U(1) symmetry in the bulk spontaneously broken on the wall. The theory on the wall is in the Coulomb phase. We explain why the mechanism of confinement discussed in the first part of the paper does not work in this case, and strings are not formed on the walls.Comment: 55 pp; v2: several remarks adde

Interplay of the volume and surface plasmons in the electron energy loss spectra of C60_{60}

The results of a joint experimental and theoretical investigation of the C60 collective excitations in the process of inelastic scattering of electrons are presented. The shape of the electron energy loss spectrum is observed to vary when the scattering angle increases. This variation arising due to the electron diffraction of the fullerene shell is described by a new theoretical model which treats the fullerene as a spherical shell of a finite width and accounts for the two modes of the surface plasmon and for the volume plasmon as well. It is shown that at small angles, the inelastic scattering cross section is determined mostly by the symmetric mode of the surface plasmon, while at larger angles, the contributions of the antisymmetric surface plasmon and the volume plasmon become prominent.Comment: 11 pages, 3 figure

Stable vs Unstable Vortices in SQCD

We give a topological classification of stable and unconfined massive particles and strings (and some instantons) in worldvolume theories of M5-branes and their dimensional reductions, generalizing Witten's classification of strings in SYM. In particular 4d N=2 SQCD softly broken to N=1 contains torsion (Douglas-Shenker) Z_N-strings and nontorsion (Hanany-Tong) Z-strings. Some of the former are stable when the flavor symmetry is gauged, while those that are not stable confine quarks and in some vacua even dyons into baryons. The nontorsion strings are stable if and only if all colors are locked to flavors, which is weaker than the BPS condition. As a byproduct unstable string decay modes and approximate lifetimes are found. Cascading theories have no vortices stabilized by the topological charges treated here and in particular Gubser-Herzog-Klebanov axionic strings do not carry such a charge.Comment: 32 pages, 6 figure

The Skyrmion strikes back: baryons and a new large NcN_c limit

In the large $N_c$ limit of QCD, baryons can be modeled as solitons, for instance, as Skyrmions. This modeling has been justified by Witten's demonstration that all properties of baryons and mesons scale with $N_c^{-1/2}$ in the same way as the analogous meson-based soliton model scales with a generic meson-meson coupling constant $g$. An alternative large $N_c$ limit (the orientifold large $N_c$ limit) has recently been proposed in which quarks transform in the two-index antisymmetric representation of $SU(N_c)$. By carrying out the analog of Witten's analysis for the new orientifold large $N_c$ limit, we show that baryons and solitons can also be identified in the orientifold large $N_c$ limit. However, in the orientifold large $N_c$ limit, the interaction amplitudes and matrix elements scale with $N_c^{-1}$ in the same way as soliton models scale with the generic meson coupling constant $g$ rather than as $N_c^{-1/2}$ as in the traditional large $N_c$ limit.Comment: 10 pages, 26 figure

Strings Inside Walls in N=1 Super Yang-Mills

We conjecture the existence of strings bounded inside walls in SU$(n)$ $\N=1$ Super Yang-Mills theory. These strings carry $\Z_{[k,n]}$ quantum number, where $[k,n]$ is the greatest common divisor between $k$, the charge of the wall, and $n$. We provide field-theoretical arguments and string-theoretical evidences, both from MQCD and from gauge-gravity correspondence. We interpret this result from the point of view of the low-energy effective action living on the $k$-wall.Comment: 25 pp. Major changes. In particular, following the recent work arXiv:0807.1908 we have been able to give a field theoretical proof of the statement. We have also corrected an important erroneous interpretation in the previous version regarding the 2+1 effective action; Typo

On The Problem of the Quantum Heterotic Vortex

We address the problem of non-Abelian super-QCD, with a Fayet-Iliopoulos term, as seen from the vortex worldsheet perspective. Together with the FI term $\xi$, also a mass $\mu$ for the adjoint superfield $\Phi$ enters in the game. This mass allows the interpolation between $\N=2$ and $\N=1$ super-QCD. While the phenomenology of the $\N=2$ case ($\mu=0$) is pretty much understood, much remains to be clarified for the finite-$\mu$ case. We distinguish, inside the parameter space spanned by the FI term and the mass $\mu$, four different corners where some quantitative statements can be made. These are the regions where the strong dynamics can, in some approximation, be quantitatively analyzed. We focus in particular on two questions: 1) Is the quantum vortex BPS or non-BPS? 2) What is the phase of the internal non-Abelian moduli? We find that the answer to these questions strongly depends upon the choice of the linear term in the superpotential. We also try to explain what happens in the most unexplored, and controversial, region of parameters, that of the quantum heterotic vortex, where $\Lambda \ll \sqrt{\xi} \ll \mu$.Comment: 47 pp; v2: typo

Degeneracy Between the Regge Slope of Mesons and Baryons from Supersymmetry

We consider the degeneracy between the Regge slope of mesons and baryons in QCD. We argue that within the "orientifold large-N approximation" asymptotically massive mesons and baryons become supersymmetric partners and hence degenerate. To this end, we generalize QCD by a SU(N) theory with a quark in the two-index antisymmetric representation. We show that in this framework the meson is represented by an oriented bosonic QCD-string and the baryon is represented by an un-oriented fermionic QCD-string. At large-N, due to an equivalence with super Yang-Mills, the tensions of the bosonic and the fermionic strings coincide. Our description of mesons and baryons as oriented and un-oriented bosonic and fermionic QCD-strings is in full agreement with the spectra of open strings in the dual type 0' string theory.Comment: v2: extended version. Appendices and references adde

Development of flood probability charts for urban drainage network in coastal areas through a simplified joint assessment approach

The operating conditions of urban drainage networks during storm events depend on the hydraulic conveying capacity of conduits and also on downstream boundary conditions. This is particularly true in coastal areas where the level of the receiving water body is directly or indirectly affected by tidal or wave effects. In such cases, not just different rainfall conditions (varying intensity and duration), but also different sea-levels and their effects on the network operation should be considered. This paper aims to study the behaviour of a seaside town storm sewer network, estimating the threshold condition for flooding and proposing a simplified method to assess the urban flooding severity as a function of climate variables. The case study is a portion of the drainage system of Rimini (Italy), implemented and numerically modelled by means of InfoWorks CS code. The hydraulic simulation of the sewerage system identified the percentage of nodes of the drainage system where flooding is expected to occur. Combining these percentages with both climate variables' values has lead to the definition of charts representing the combined degree of risk "rainfall-sea level" for the drainage system under investigation. A final comparison between such charts and the results obtained from a one-year rainfall-sea level time series has demonstrated the reliability of the analysis

Hyperbolic monopoles, JNR data and spectral curves

A large class of explicit hyperbolic monopole solutions can be obtained from JNR instanton data, if the curvature of hyperbolic space is suitably tuned. Here we provide explicit formulae for both the monopole spectral curve and its rational map in terms of JNR data. Examples with platonic symmetry are presented, together with some one-parameter families with cyclic and dihedral symmetries. These families include hyperbolic analogues of geodesics that describe symmetric monopole scatterings in Euclidean space and we illustrate the results with energy density isosurfaces. There is a metric on the moduli space of hyperbolic monopoles, defined using the Abelian connection on the boundary of hyperbolic space, and we provide a simple integral formula for this metric on the space of JNR data

Type I Non-Abelian Superconductors in Supersymmetric Gauge Theories

Non-BPS non-Abelian vortices with CP^1 internal moduli space are studied in an N=2 supersymmetric U(1) x SU(2) gauge theory with softly breaking adjoint mass terms. For generic internal orientations the classical force between two vortices can be attractive or repulsive. On the other hand, the mass of the scalars in the theory is always less than that of the vector bosons; also, the force between two vortices with the same CP^1 orientation is always attractive: for these reasons we interpret our model as a non-Abelian generalization of type I superconductors. We compute the effective potential in the limit of two well separated vortices. It is a function of the distance and of the relative colour-flavour orientation of the two vortices; in this limit we find an effective description in terms of two interacting CP^1 sigma models. In the limit of two coincident vortices we find two different solutions with the same topological winding and, for generic values of the parameters, different tensions. One of the two solutions is described by a CP^1 effective sigma model, while the other is just an Abelian vortex without internal degrees of freedom. For generic values of the parameters, one of the two solutions is metastable, while there are evidences that the other one is truly stable.Comment: 35 pages, 8 figures. v2: fixed typos and added small comments, v3 removed an unecessary figur