Solitons in the Higgs phase -- the moduli matrix approach --

We review our recent work on solitons in the Higgs phase. We use U(N_C) gauge theory with N_F Higgs scalar fields in the fundamental representation, which can be extended to possess eight supercharges. We propose the moduli matrix as a fundamental tool to exhaust all BPS solutions, and to characterize all possible moduli parameters. Moduli spaces of domain walls (kinks) and vortices, which are the only elementary solitons in the Higgs phase, are found in terms of the moduli matrix. Stable monopoles and instantons can exist in the Higgs phase if they are attached by vortices to form composite solitons. The moduli spaces of these composite solitons are also worked out in terms of the moduli matrix. Webs of walls can also be formed with characteristic difference between Abelian and non-Abelian gauge theories. We characterize the total moduli space of these elementary as well as composite solitons. Effective Lagrangians are constructed on walls and vortices in a compact form. We also present several new results on interactions of various solitons, such as monopoles, vortices, and walls. Review parts contain our works on domain walls (hep-th/0404198, hep-th/0405194, hep-th/0412024, hep-th/0503033, hep-th/0505136), vortices (hep-th/0511088, hep-th/0601181), domain wall webs (hep-th/0506135, hep-th/0508241, hep-th/0509127), monopole-vortex-wall systems (hep-th/0405129, hep-th/0501207), instanton-vortex systems (hep-th/0412048), effective Lagrangian on walls and vortices (hep-th/0602289), classification of BPS equations (hep-th/0506257), and Skyrmions (hep-th/0508130).Comment: 89 pages, 33 figures, invited review article to Journal of Physics A: Mathematical and General, v3: typos corrected, references added, the published versio

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

Sudden To Adiabatic Transition in Beta Decay

We discuss effects in beta decays at very low beta energies, of the order of the kinetic energies of atomic electrons. As the beta energy is lowered the atomic response changes from sudden to adiabatic. As a consequence, the beta decay rate increases slightly and the ejection of atomic electrons (shake off) and subsequent production of X rays is turned off. We estimate the transition energy and the change in decay rate. The rate increase is largest in heavy atoms, which have a small Q value in their decay. The X ray switch-off is independent of Q value.Comment: 6 pages LaTe

Massless Localized Vector Field on a Wall in D=5 SQED with Tensor Multiplets

Massless localized vector field is obtained in five-dimensional supersymmetric (SUSY) QED coupled to tensor multiplets as a half BPS solution. The four-dimensional gauge coupling is obtained as a topological charge. We also find all the (bosonic) massive modes exactly for a particular value of a parameter, demonstrating explicitly the existence of a mass gap. The four-dimensional Coulomb law is shown to hold for sources placed on the wall.Comment: 18 pages, 3 figures, First version is completely replaced due to an error of submitting a different pape

Vortex Strings and Four-Dimensional Gauge Dynamics

We study the low-energy quantum dynamics of vortex strings in the Higgs phase of N=2 supersymmetric QCD. The exact BPS spectrum of the stretched string is shown to coincide with the BPS spectrum of the four-dimensional parent gauge theory. Perturbative string excitations correspond to bound W-bosons and quarks while the monopoles appear as kinks on the vortex string. This provides a physical explanation for an observation by N. Dorey relating the quantum spectra of theories in two and four dimensions.Comment: 23 pages, 1 figure. v2: Two extra appendices included: one on the brane construction, the other describing the potential on the vortex moduli space. Two figures added. Typos corrected and references added. v3: BPS nature of quarks correcte

Relativistic Calculation of two-Electron one-Photon and Hypersatellite Transition Energies for 12≤Z≤3012\leq Z\leq30 Elements

Energies of two-electron one-photon transitions from initial double K-hole states were computed using the Dirac-Fock model. The transition energies of competing processes, the K$\alpha$ hypersatellites, were also computed. The results are compared to experiment and to other theoretical calculations.Comment: accepted versio

Dark matter production from cosmic necklaces

Cosmic strings have gained a great interest, since they are formed in a large class of brane inflationary models. The most interesting story is that cosmic strings in brane models are distinguished in future cosmological observations. If the strings in brane models are branes or superstrings that can move along compactified space, and also if there are degenerated vacua along the compactified space, kinks interpolate between degenerated vacua become ``beads'' on the strings. In this case, strings turn into necklaces. In the case that the compact manifold in not simply connected, a string loop that winds around a nontrivial circle is stable due to the topological reason. Since the existence of the (quasi-)degenerated vacua and the nontrivial circle is a common feature of the brane models, it is important to study cosmological constraints on the cosmic necklaces and the stable winding states. In this paper, we consider dark matter production from loops of the cosmic necklaces. Our result suggests that necklaces can put stringent bound on certain kinds of brane models.Comment: 27 pages, 5 figures, added many comments and 3 figures, accepted for publication in JCA

Elliptic Inflation: Generating the curvature perturbation without slow-roll

There are many inflationary models in which inflaton field does not satisfy the slow-roll condition. However, in such models, it is always difficult to generate the curvature perturbation during inflation. Thus, to generate the curvature perturbation, one must introduce another component to the theory. To cite a case, curvatons may generate dominant part of the curvature perturbation after inflation. However, we have a question whether it is unrealistic to consider the generation of the curvature perturbation during inflation without slow-roll. Assuming multi-field inflation, we encounter the generation of the curvature perturbation during inflation without slow-roll. The potential along equipotential surface is flat by definition and thus we do not have to worry about symmetry. We also discuss about KKLT models, in which corrections lifting the inflationary direction may not become a serious problem if there is a symmetry enhancement at the tip (not at the moving brane) of the inflationary throat.Comment: 27pages, 8figures, to appear in JCA

Domain Walls with Non-Abelian Clouds

Domain walls in U(N) gauge theories, coupled to Higgs scalar fields with degenerate masses, are shown to possess normalizable non-Abelian Nambu-Goldstone(NG) modes, which we call non-Abelian clouds. We construct the moduli space metric and its Kahler potential of the effective field theory on the domain walls, by focusing on two models: a U(1) gauge theory with several charged Higgs fields, and a U(N) gauge theory with 2N Higgs fields in the fundamental representation. We find that non-Abelian clouds spread between two domain walls and that their rotation induces long-range repulsive force, in contrast to a U(1) mode in models with fully non-degenerate masses which gives short-range force. We also construct a bound state of dyonic domain walls by introducing the imaginary part of the Higgs masses. In the latter model we find that when all walls coincide SU(N)_L x SU(N)_R x U(1) symmetry is broken down to SU(N)_V, and U(N)_A NG modes and the same number of quasi-NG modes are localized on the wall. When n walls separate, off diagonal elements of U(n) NG modes have wave functions spreading between two separated walls (non-Abelian clouds), whereas some quasi-NG modes turn to NG bosons as a result of further symmetry breaking U(n)_V --> U(1)_V^n. In the case of 4+1 dimensional bulk, we can dualize the effective theory to the supersymmetric Freedman-Townsend model of non-Abelian 2-form fields.Comment: 43 pages, 18 figures, v2: minor change

Vortices on Orbifolds

The Abelian and non-Abelian vortices on orbifolds are investigated based on the moduli matrix approach, which is a powerful method to deal with the BPS equation. The moduli space and the vortex collision are discussed through the moduli matrix as well as the regular space. It is also shown that a quiver structure is found in the Kahler quotient, and a half of ADHM is obtained for the vortex theory on the orbifolds as the case before orbifolding.Comment: 25 pages, 4 figures; references adde