We study localization of bulk fermions on a string-like defect with the exponentially decreasing warp factor in six dimensions with inclusion of U(1) gauge background from the viewpoint of field theory, and give the conditions under which localized spin 1/2 and 3/2 fermions can be obtained.

In this paper, we study localization and mass spectrum of various matter fields on a family of thick brane configurations in a pure geometric Weyl integrable 5-dimensional space time, a non-Riemannian modification of 5-dimensional Kaluza–Klein(KK) theory. We present the shape of the mass-independent potential of the corresponding Schrodinger problem and obtain the KK modes and mass spectrum, where a special coupling of spinors and scalars is considered for fermions. It is shown that, for a class of brane configurations, there exists a continuum gapless spectrum of KK modes with any m2>0 for scalars, vectors and ones of left chiral and right chiral fermions. All of the corresponding massless modes are found to be normalizable on the branes. However, for a special of brane configuration, the corresponding effective Schrodinger equations have modified Poschl-Teller potentials. These potentials suggest that there exist mass gap and a series of continuous spectrum starting at positive m2. There are one bound state for spin one vectors, which is just the normalizable vector zero mode, and two bound KK modes for scalars. The total number of bound states for spin half fermions is determined by the coupling constant. In the case of no coupling (= 0), there are no any localized fermion KK modes including zero modes for both left and right chiral fermions. For positive (negative) coupling constant, the number of bound states of right chiral fermions is one less (more) than that of left chiral fermions. In both cases (>0 and<0), only one of the zero modes for left chiral fermions and right chiral fermions is bound and normalizable.

A three-parameter (positive odd integers, thickness factor, and asymmetry factora) family of asymmetric thick brane solutions in five dimensions were constructed from a two-parameter (s and) family of symmetric ones in [R. Guerrero, R.O. Rodriguez, and R. Torrealba, Phys. Rev. D72, 124012 (2005).]. The values s = 1 and s 3 correspond to single branes and double branes,respectively. These branes have very rich inner structure. In this paper, by presenting the massindependent potentials of Kaluza–Klein (KK) modes in the corresponding Schrodinger equations,we investigate the localization and mass spectra of fermions on the symmetric and asymmetric thick branes in an AdS background. In order to analyze the effect of gravity-fermion interaction (i.e., the effect of the inner structure of the branes) and scalar-fermion interaction to the spectrum of fermion KK modes, we consider three kinds of typical kink-fermion couplings. The spectra of left chiral fermions for these couplings are consisted of a bound zero mode and a series of gapless continuous massive KK modes, some discrete bound KK modes including zero mode (exist mass gaps) and a series of continuous massive KK modes, infinite discrete bound KK modes, respectively. The structures of the spectra are investigated in detail.

By making use of the decomposition of U(1) gauge potential theory and the-mapping method,we propose that a charged two-condensate Bose system possesses vortex lines and two classes of knotted solitons. The topological charges of the vortex lines are characterized by the Hopf indices and the Brower degrees of-mapping, and the knotted solitons are described by the nontrivial Hopf invariant and the BF action, respectively.

It has been shown that certain W algebras can be linearized by the inclusion of a spin-1 current. This Provides a way of obtaining new realizations of the W algebras. In this paper, we investigate the new ghost field realizations of the W2,s(s = 3, 4) algebras, making use of the fact that these two algebras can be linearized. We then construct the nilpotent BRST charges of the spinor non-critical W2,s strings with these new realizations.