Gauge Fields, Fermions and Mass Gaps in 6D Brane Worlds

We study fluctuations about axisymmetric warped brane solutions in 6D minimal gauged supergravity. Much of our analysis is general and could be applied to other scenarios. We focus on bulk sectors that could give rise to Standard Model gauge fields and charged matter. We reduce the dynamics to Schroedinger type equations plus physical boundary conditions, and obtain exact solutions for the Kaluza-Klein wave functions and discrete mass spectra. The power-law warping, as opposed to exponential in 5D, means that zero mode wave functions can be peaked on negative tension branes, but only at the price of localizing the whole Kaluza-Klein tower there. However, remarkably, the codimension two defects allow the Kaluza-Klein mass gap to remain finite even in the infinite volume limit. In principle, not only gravity, but Standard Model fields could `feel' the extent of large extra dimensions, and still be described by an effective 4D theory.Comment: 33 pages, 2 figures; typesetting problem fixed ({\o}replaced by \omega

On the Decoupling of Heavy Modes in Kaluza-Klein Theories

In this paper we examine the 4-dimensional effective theory for the light Kaluza-Klein (KK) modes. Our main interest is in the interaction terms. We point out that the contribution of the heavy KK modes is generally needed in order to reproduce the correct predictions for the observable quantities involving the light modes. As an example we study in some detail a 6-dimensional Einstein-Maxwell theory coupled to a charged scalar and fermions. In this case the contribution of the heavy KK modes are geometrically interpreted as the deformation of the internal space.Comment: 38 pages, 1 figur

Dirac Fermions and Domain Wall Defects in 2+1 Dimensions

We investigate some properties of a system of Dirac fermions in 2+1 dimensions, with a space dependent mass having domain wall like defects.These defects are defined by the loci of the points where the mass changes sign. In general, they will be curves lying on the spatial plane. We show how to treat the dynamics of the fermions in such a way that the existence of localized fermionic zero modes on the defects is transparent. Moreover, effects due to the higher, non zero modes, can be quantitatively studied. We also consider the relevance of the profile of the mass near the region where it changes sign. Finally, we apply our general results to the calculation of the induced fermionic current, in the linear response approximation, in the presence of an external electric field and defects.Comment: 23 pages, 1 Postscript figur

Localizing gravity on a 't Hooft-Polyakov monopole in seven dimensions

We present regular solutions for a brane world scenario in the form of a 't Hooft-Polyakov monopole living in the three-dimensional spherical symmetric transverse space of a seven-dimensional spacetime. In contrast to the cases of a domain-wall in five dimensions and a string in six dimensions, there exist gravity-localizing solutions for both signs of the bulk cosmological constant. A detailed discussion of the parameter space that leads to localization of gravity is given. A point-like monopole limit is discussed.Comment: 29 pages, 17 figure

Dimensional Reduction of the 5D Kaluza-Klein Geodesic Deviation Equation

In the work of Kerner et al. (2001) the problem of the geodesic deviation in a 5D Kaluza Klein background is faced. The 4D space-time projection of the resulting equation coincides with the usual geodesic deviation equation in the presence of the Lorenz force, provided that the fifth component of the deviation vector satisfies an extra constraint which takes into account the $q/m$ conservation along the path. The analysis was performed setting as a constant the scalar field which appears in Kaluza-Klein model. Here we focus on the extension of such a work to the model where the presence of the scalar field is considered. Our result coincides with that of Kerner et al. when the minimal case $\phi=1$ is considered, while it shows some departures in the general case. The novelty due to the presence of $\phi$ is that the variation of the $q/m$ between the two geodesic lines is not conserved during the motion; an exact law for such a behaviour has been derived.Comment: 9 page

Brane Gravitational Interactions from 6D Supergravity

We investigate the massive graviton contributions to 4D gravity in a 6D brane world scenario, whose bulk field content can include that of 6D chiral gauged supergravity. We consider a general class of solutions having 3-branes, 4D Poincare symmetry and axisymmetry in the internal space. We show that these contributions, which we compute analytically, can be independent of the brane vacuum energy as a consequence of geometrical and topological properties of the above-mentioned codimension two brane world. These results support the idea that in such models the gravitational interactions may be decoupled from the brane vacuum energy.Comment: 13 pages, 4 figure

The Fuzzy Ginsparg-Wilson Algebra: A Solution of the Fermion Doubling Problem

The Ginsparg-Wilson algebra is the algebra underlying the Ginsparg-Wilson solution of the fermion doubling problem in lattice gauge theory. The Dirac operator of the fuzzy sphere is not afflicted with this problem. Previously we have indicated that there is a Ginsparg-Wilson operator underlying it as well in the absence of gauge fields and instantons. Here we develop this observation systematically and establish a Dirac operator theory for the fuzzy sphere with or without gauge fields, and always with the Ginsparg-Wilson algebra. There is no fermion doubling in this theory. The association of the Ginsparg-Wilson algebra with the fuzzy sphere is surprising as the latter is not designed with this algebra in mind. The theory reproduces the integrated U(1)_A anomaly and index theory correctly.Comment: references added, typos corrected, section 4.2 simplified. Report.no: SU-4252-769, DFUP-02-1

Magnetic moment interaction in the anyon superconductor

Magnetic moment interaction is shown to play a defining role in the magnetic properties of anyon superconductors. The necessary condition for the existence of the Meissner effect is found.Comment: 4 pages, Revtex, to appear in Phys. Rev. B, corrected typo