Field theory simulation of Abelian-Higgs cosmic string cusps

We have performed a lattice field theory simulation of cusps in Abelian-Higgs cosmic strings. The results are in accord with the theory that the portion of the strings which overlaps near the cusp is released as radiation. The radius of the string cores which must touch to produce the evaporation is approximately $r = 1$ in natural units. In general, the modifications to the string shape due to the cusp may produce many cusps later in the evolution of a string loop, but these later cusps will be much smaller in magnitude and more closely resemble kinks.Comment: 9 pages, RevTeX, 13 figures with eps

Fast Hybrid Algorithms For High Frequency Scattering

This paper deals with numerical methods for high frequency wave scattering. It introduces a new hybrid technique that couples a directional fast multipole method for a subsection of it scattering surface to an asymptotic formulation over the rest of the scattering domain. The directional fast multipole method is new and highly efficient for the solution of the boundary integral formulation of a general scattering problem but it requires at least a few unknowns per wavelength on the boundary. The asymptotic method that was introduced by Bruno and collaborators requires much fewer unknowns. Oil the other hand the scattered field must have a simple structure. Hybridization of these two methods retains their best properties for the solution of the full problem, Numerical examples are given for the solution of the Helmholtz equation in two space dimensions.Mathematic

Rational three-spin string duals and non-anomalous finite size effects

We determine by a one line computation the one-loop conformal dimension and the associated non-anomalous finite size correction for all operators dual to spinning strings of rational type having three angular momenta (J_1,J_2,J_3) on S^5. Finite size corrections are conjectured to encode information about string sigma model loop corrections to the spectrum of type IIB superstrings on AdS_5xS^5. We compare our result to the zero-mode contribution to the leading quantum string correction derived for the stable three-spin string with two out of the three spin labels identical and observe agreement. As a side result we clarify the relation between the Bethe root description of three-spin strings of the type (J,J',J') with respectively J>J' and J<J'.Comment: 15 pages, v2: comparison to string theory changed, references added, v3: textual modifications and title change

A dual lagrangian for non-Abelian tensor gauge fields

For non-Abelian tensor gauge fields of the lower rank we have found an alternative expression for the field strength tensors, which transform homogeneously with respect to the complementary gauge transformations and allow us to construct the dual Lagrangian.Comment: 13 pages, LaTex fil

Holography of the N=1 Higher-Spin Theory on AdS4

We argue that the N=1 higher-spin theory on AdS4 is holographically dual to the N=1 supersymmetric critical O(N) vector model in three dimensions. This appears to be a special form of the AdS/CFT correspondence in which both regular and irregular bulk modes have similar roles and their interplay leads simultaneously to both the free and the interacting phases of the boundary theory. We study various boundary conditions that correspond to boundary deformations connecting, for large-N, the free and interacting boundary theories. We point out the importance of parity in this holography and elucidate the Higgs mechanism responsible for the breaking of higher-spin symmetry for subleading N.Comment: 19 page

Matching Higher Conserved Charges for Strings and Spins

We demonstrate that the recently found agreement between one-loop scaling dimensions of large dimension operators in N=4 gauge theory and energies of spinning strings on AdS_5 x S^5 extends to the eigenvalues of an infinite number of hidden higher commuting charges. This dynamical agreement is of a mathematically highly intricate and non-trivial nature. In particular, on the gauge side the generating function for the commuting charges is obtained by integrable quantum spin chain techniques from the thermodynamic density distribution function of Bethe roots. On the string side the generating function, containing information to arbitrary loop order, is constructed by solving exactly the Backlund equations of the integrable classical string sigma model. Our finding should be an important step towards matching the integrable structures on the string and gauge side of the AdS/CFT correspondence.Comment: Latex, 33 pages, v2: new section added (completing the analytic proof that the entire infinite towers of commuting gauge and string charges match); references adde

On the worldsheet theories of strings dual to free large N gauge theories

We analyze in detail some properties of the worldsheet of the closed string theories suggested by Gopakumar to be dual to free large N SU(N) gauge theories (with adjoint matter fields). We use Gopakumar's prescription to translate the computation of space-time correlation functions to worldsheet correlation functions for several classes of Feynman diagrams, by explicit computations of Strebel differentials. We compute the worldsheet operator product expansion in several cases and find that it is consistent with general worldsheet conformal field theory expectations. A peculiar property of the construction is that in several cases the resulting worldsheet correlation functions are non-vanishing only on a sub-space of the moduli space (say, for specific relations between vertex positions). Another strange property we find is that for a conformally invariant space-time theory, the mapping to the worldsheet does not preserve the special conformal symmetries, so that the full conformal group is not realized as a global symmetry on the worldsheet (even though it is, by construction, a symmetry of all integrated correlation functions).Comment: 60 pages, 17 figures, latex. v2: Added references and a minor correctio

Circular and Folded Multi-Spin Strings in Spin Chain Sigma Models

From the SU(2) spin chain sigma model at the one-loop and two-loop orders we recover the classical circular string solution with two S^5 spins (J_1, J_2) in the AdS_5 x S^5 string theory. In the SL(2) sector of the one-loop spin chain sigma model we explicitly construct a solution which corresponds to the folded string solution with one AdS_5 spin S and one S^5 spin J. In the one-loop general sigma model we demonstrate that there exists a solution which reproduces the energy of the circular constant-radii string solution with three spins (S_1, S_2, J).Comment: 16 pages, LaTeX, no figure

Classical/quantum integrability in non-compact sector of AdS/CFT

We discuss non-compact SL(2,R) sectors in N=4 SYM and in AdS string theory and compare their integrable structures. We formulate and solve the Riemann-Hilbert problem for the finite gap solutions of the classical sigma model and show that at one loop it is identical to the classical limit of Bethe equations of the spin (-1/2) chain for the dilatation operator of SYM.Comment: 27 pages, 1 figure; v2: unphysical windings around the time direction eliminated; v3: dicsussion of finite-size corrections remove

Role of phason-defects on the conductance of a 1-d quasicrystal

We have studied the influence of a particular kind of phason-defect on the Landauer resistance of a Fibonacci chain. Depending on parameters, we sometimes find the resistance to decrease upon introduction of defect or temperature, a behavior that also appears in real quasicrystalline materials. We demonstrate essential differences between a standard tight-binding model and a full continuous model. In the continuous case, we study the conductance in relation to the underlying chaotic map and its invariant. Close to conducting points, where the invariant vanishes, and in the majority of cases studied, the resistance is found to decrease upon introduction of a defect. Subtle interference effects between a sudden phason-change in the structure and the phase of the wavefunction are also found, and these give rise to resistive behaviors that produce exceedingly simple and regular patterns.Comment: 12 pages, special macros jnl.tex,reforder.tex, eqnorder.tex. arXiv admin note: original tex thoroughly broken, figures missing. Modified so that tex compiles, original renamed .tex.orig in source