Quasi-localized states on noncommutative solitons

We consider noncommutative gauge theories which have zero mass states propagating along both commutative and noncommutative dimensions. Solitons in these theories generically carry U(m) gauge group on their world-volume. From the point of view of string theory, these solitons correspond to ``branes within branes''. We show that once the world-volume U(m) gauge theory is in the Higgs phase, light states become quasi-localized, rather than strictly localized on the soliton, i.e. they mix with light bulk modes and have finite widths to escape into the noncommutative dimensions. At small values of U(m) symmetry breaking parameters, these widths are small compared to the corresponding masses. Explicit examples considered are adjoint scalar field in the background of a noncommutative vortex in U(1)-Higgs theory, and gauge fields in instanton backgrounds in pure gauge noncommutative theories.Comment: 27 pages, references and comments added, final version to appear in JHE

Domain walls between gauge theories

Noncommutative U(N) gauge theories at different N may be often thought of as different sectors of a single theory: the U(1) theory possesses a sequence of vacua labeled by an integer parameter N, and the theory in the vicinity of the N-th vacuum coincides with the U(N) noncommutative gauge theory. We construct noncommutative domain walls on fuzzy cylinder, separating vacua with different gauge theories. These domain walls are solutions of BPS equations in gauge theory with an extra term stabilizing the radius of the cylinder. We study properties of the domain walls using adjoint scalar and fundamental fermion fields as probes. We show that the regions on different sides of the wall are not disjoint even in the low energy regime -- there are modes penetrating from one region to the other. We find that the wall supports a chiral fermion zero mode. Also, we study non-BPS solution representing a wall and an antiwall, and show that this solution is unstable. We suggest that the domain walls emerge as solutions of matrix model in large class of pp-wave backgrounds with inhomogeneous field strength. In the M-theory language, the domain walls have an interpretation of a stack of branes of fingerstall shape inserted into a stack of cylindrical branes.Comment: Final version; minor corrections; to appear in Nucl.Phys.

Localisation and mass generation for non-Abelian gauge fields

It has been suggested recently that in the presence of suitably "warped" extra dimensions, the low-energy limit of pure gauge field theory may contain massive elementary vector bosons localised on a "brane", but no elementary Higgs scalars. We provide non-perturbative evidence in favour of this conjecture through numerical lattice measurements of the static quark-antiquark force of pure SU(2) gauge theory in three dimensions, of which one is warped. We consider also warpings leading to massless localised vector bosons, and again find evidence supporting the perturbative prediction, even though the gauge coupling diverges far from the brane in this case.Comment: 27 pages; small clarifications adde

Primary decomposition and the fractal nature of knot concordance

For each sequence of polynomials, P=(p_1(t),p_2(t),...), we define a characteristic series of groups, called the derived series localized at P. Given a knot K in S^3, such a sequence of polynomials arises naturally as the orders of certain submodules of the sequence of higher-order Alexander modules of K. These group series yield new filtrations of the knot concordance group that refine the (n)-solvable filtration of Cochran-Orr-Teichner. We show that the quotients of successive terms of these refined filtrations have infinite rank. These results also suggest higher-order analogues of the p(t)-primary decomposition of the algebraic concordance group. We use these techniques to give evidence that the set of smooth concordance classes of knots is a fractal set. We also show that no Cochran-Orr-Teichner knot is concordant to any Cochran-Harvey-Leidy knot.Comment: 60 pages, added 4 pages to introduction, minor corrections otherwise; Math. Annalen 201

Exact noncommutative solitons in p-adic strings and BSFT

The tachyon field of p-adic string theory is made noncommutative by replacing ordinary products with noncommutative products in its exact effective action. The same is done for the boundary string field theory, treated as the p -> 1 limit of the p-adic string. Solitonic lumps corresponding to D-branes are obtained for all values of the noncommutative parameter theta. This is in contrast to usual scalar field theories in which the noncommutative solitons do not persist below a critical value of theta. As theta varies from zero to infinity, the solution interpolates smoothly between the soliton of the p-adic theory (respectively BSFT) to the noncommutative soliton.Comment: 1+14 pages (harvmac b), 1 eps figure, v2: references added, typos correcte

Operator algebra quantum homogeneous spaces of universal gauge groups

In this paper, we quantize universal gauge groups such as SU(\infty), as well as their homogeneous spaces, in the sigma-C*-algebra setting. More precisely, we propose concise definitions of sigma-C*-quantum groups and sigma-C*-quantum homogeneous spaces and explain these concepts here. At the same time, we put these definitions in the mathematical context of countably compactly generated spaces as well as C*-compact quantum groups and homogeneous spaces. We also study the representable K-theory of these spaces and compute it for the quantum homogeneous spaces associated to the universal gauge group SU(\infty).Comment: 14 pages. Merged with [arXiv:1011.1073

Tachyon Kinks in Boundary String Field Theory

We study tachyon kinks with and without electromagnetic fields in the context of boundary string field theory. For the case of pure tachyon only an array of kink-antikink is obtained. In the presence of electromagnetic coupling, all possible static codimension-one soliton solutions such as array of kink-antikink, single topological BPS kink, bounce, half kink, as well as nonBPS topological kink are found, and their properties including the interpretation as branes are analyzed in detail. Spectrum of the obtained kinks coincides with that of Dirac-Born-Infeld type effective theory.Comment: LaTex, 29 pages, 17 Figure

Phase structure of non-commutative scalar field theories

We investigate the phase structure of non-commutative scalar field theories and find evidence for ordered phases which break translation invariance. A self-consistent one-loop analysis indicates that the transition into these ordered phases is first order. The phase structure and the existence of scaling limits provides an alternative to the structure of counter-terms in determining the renormalizability of non-commutative field theories. On the basis of the existence of a critical point in the closely related planar theory, we argue that there are renormalizable interacting non-commutative scalar field theories in dimensions two and above. We exhibit this renormalization explicitly in the large $N$ limit of a non-commutative O(N) vector model.Comment: 33 pages, latex. v2: minor improvements, version to appear in NP

N D0-branes and antibranes in the background independent string field theory

In this paper we extend our previous work hep-th/0102063 to the case D0-brane+antibrane system.Comment: 20 page

The Relationship Between Plasma Flow Doppler Velocities and Magnetic Field Parameters During the Emergence of Active Regions at the Solar Photospheric Level

A statistical study has been carried out of the relationship between plasma flow Doppler velocities and magnetic field parameters during the emergence of active regions at the solar photospheric level with data acquired by the Michelson Doppler Imager (MDI) onboard the Solar and Heliospheric Observatory (SOHO). We have investigated 224 emerging active regions with different spatial scales and positions on the solar disc. The following relationships for the first hours of the emergence of active regions have been analysed: i) of peak negative Doppler velocities with the position of the emerging active regions on the solar disc; ii) of peak plasma upflow and downflow Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the solar disc centre (the vertical component of plasma flows); iii) of peak positive and negative Doppler velocities with the magnetic flux growth rate and magnetic field strength for the active regions emerging near the limb (the horizontal component of plasma flows); iv) of the magnetic flux growth rate with the density of emerging magnetic flux; v) of the Doppler velocities and magnetic field parameters for the first hours of the appearance of active regions with the total unsigned magnetic flux at the maximum of their development.Comment: 14 pages, 8 figures. The results of article were presented at the ESPM-13 (12-16 September 2011, Rhodes, Greece, Abstract Book p. 102-103, P.4.13, http://astro.academyofathens.gr/espm13/documents/ESPM13_abstract_programme_book.pdf