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.

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.

Motivated by the recent work on the fermion resonances on scalar-constructed thick branes (arXiv:0901.3543 and arXiv:0904.1785), we extend the idea to multi-scalar generated thick branes and complete previous work. The fermion localization and resonances on the three-field and two-field thick branes are investigated. With the Numerov method, our numerical results show that the resonance states also exist in the brane besides the single-field thick branes and the two-field thick branes in the former cases. This interesting phenomenon is related to the internal structure of the brane and the coupling of fermions and scalars. We find that the Kaluza-Klein chiral decomposition of massive fermion resonances is the parity-chiral decomposition. For the couplings k and k for three-field and two-field models with odd positive k,respectively, the number of the resonant states decreases with k. This result is opposite to the one obtained in the single-field de Sitter thick brane (arXiv:0904.1785).

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.

In 1997, Liberati and Pollifrone in Phys. Rev. D56 (1997) 6458 (hep-th/9708014) achieved a new formulation of the Bekenstein-Hawking formula, where the entropy and the Euler characteristic are related by S = A/8. In this work we present a relation between the low-energy absorption cross section for minimally coupled fermions and the Euler characteristic of (3+1)-dimensional spherically symmetric black holes, i.e.=g−1 h A. Based on the relation, using the Gauss–Bonnet–Chern theorem and the -mapping method, an absorption cross section density is introduced to describe the topology of the absorption cross section. It is shown that the absorption cross section and its density are determined by the singularities of the timelike Killing vector field of the spacetime and these singularities carry the topological numbers, Hopf indices and Brouwer degrees, naturally.