By using the self-dual vortex background on extra two-dimensional Riemann surfaces in 5+1 dimensions, the localization mechanism of bulk fermions on a string-like defect with the exponentially decreasing warp-factor is obtained. We give the conditions under which localized spin 1/2 and 3/2 fermions can be obtained.

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.

A class of thick branes in the background of sine-Gordon kinks with a scalar potential V(φ)=p(1+cos) was constructed by R. Koley and S. Kar [Classical Quantum Gravity 22, 753 (2005)]. In this paper, in the background of the warped geometry, we investigate the issue of localization of spin-1=2 fermions on these branes in the presence of two types of scalar-fermion couplings: and sin. By presenting the mass-independent potentials in the corresponding Schro¨dinger equations, we obtain the lowest Kaluza-Klein modes and a continuous gapless spectrum of Kaluza-Klein states with m2>0 for both types of couplings. For the Yukawa coupling, the effective potential of the right chiral fermions for positive q and is always positive; hence only the effective potential of the left chiral fermions could trap the corresponding zero mode. This is a well-known conclusion which is discussed extensively in the literature. However, for the coupling sin, the effective potential of the right chiral fermions for positive q and is no longer always positive. Although the value of the potential at the location of the brane is still positive, it has a series of wells and barriers on each side, which ensures that the right chiral fermion zero mode could be trapped. Thus we may draw the following remarkable conclusion: for positive and q,the potentials of both the left and right chiral fermions could trap the corresponding zero modes under certain restrictions.

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.

The grading Becchi-Rouet-Stora-Tyutin (BRST) method gives a way to construct the integer W2,s strings, where the BRST charge is written as QB= Q0 +Q1. Using this method, we reconstruct the nilpotent BRST charges Q0 for the integer W2,s strings and the half-integer W2,s strings. Then we construct the exact grading BRST charge with spinor fields and give the new realizations of the half-integer W2,s strings for the cases of s= 3/2, 5/2, and 7/2.