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.

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.

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.

In Phys. Rev. D 78 (2008) 104018 [arXiv:0807.1481], the conclusion that“entropy eigenvalues of GB black hole are discrete and equally spaced, but the area spacing is not equidistant” was firstly presented by Kothawala, Padmanabhan and Sarkar. In this paper, using the new physical interpretation of quasinormal modes proposed by Maggiore,we calculate the quantum spectra of entropy for various types of non-rotating black holes with no charge. The spectrum is obtained by imposing Bohr-Sommerfeld quantization condition to the adiabatic invariant quantity. We conjecture that the spacing of entropy spectrum is equidistant and is independent of the dimension of spacetime. However, the spacing of area spectrum depends on gravity theory. In Einstein’s gravity, it is equally spaced, otherwise it is non-equidistant. This conjecture agrees with the result of Kothawala,Padmanabhan and Sarkar.

In arXiv:0901.3543, the simplest Yukawa coupling was considered for a two-scalargenerated Bloch brane model. Fermionic resonances for both chiralities were obtained, and their appearance is related to branes with internal structure. Inspired on this result, we investigate the localization and resonance spectrum of fermions on a one-scalar-generated dS thick brane with a class of scalar-fermion couplings-k with positive odd integer k. A set of massive fermionic resonances for both chiralities are obtained when provided large couple constant. We find that the masses and life-times of left and right chiral resonances are almost the same, which demonstrates that it is possible to compose massive Dirac fermions from the left and right chiral resonances.The resonance with lower mass has longer life-time. For a same set of parameters, the number of resonances increases with k and the life-time of the lower level resonance for larger k is much longer than the one for smaller k.