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.

The first order perturbations of the energy levels of a stationary hydrogen atom in static external gravitational field, with Schwarzschild metric, are investigated. The energy shifts are calculated for the relativistic 1S, 2S, 2P, 3S, 3P, 3D, 4S, 4P, 4D and 4F levels. The results show that the energy-level shifts of the states with total angular momentum quantum number 1/2 are all zero, and the ratio of absolute energy shifts with total angular momentum quantum number 5/2 is 1:4:5. This feature can be used to help us to distinguish the gravitational effect from other effect.

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.

In this paper, we construct the nilpotent Becchi-Rouet-Stora-Tyutin(BRST) charges of spinor non-critical W2,s strings. The cases of s = 3, 4 are discussed in detail, and spinor realization for s = 4 is given explicitly. The BRST charges are graded.

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.

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.

An asymmetric thick domain wall solution with de Sitter (dS) expansion in five dimensions can be constructed from a symmetric one by using a same scalar (kink) with different potentials. In this paper, by presenting the mass-independent potentials of Kaluza–Klein (KK) modes in the corresponding Schröodinger equations, we investigate the localization and mass spectra of various bulk matter fields on the symmetric and asymmetric dS thick branes. For spin 0 scalars and spin 1 vectors, the potentials of KK modes in the corresponding Schrodinger equations are the modified P¨oschl-Teller potentials, and there exist a mass gap and a series of continuous spectrum. It is shown that the spectrum of scalar KK modes on the symmetric dS brane contains only one bound mode (the massless mode). However, for the asymmetric dS brane with a large asymmetric factor, there are two bound scalar KK modes: a zero mode and a massive mode. For spin 1 vectors, the spectra of KK modes on both dS branes consist of a bound massless mode and a set of continuous ones, i.e., the asymmetric factor does not change the number of the bound vector KK modes. For spin 1/2 fermions, two types of kink-fermion couplings are investigated in detail. For the usual Yukawa coupling, there exists no mass gap but a continuous gapless spectrum of KK states. For the scalar-fermion couplingsin(0) cos−(0) with a positive coupling constant, there exist some discrete bound KK modes and a series of continuous ones. The total number of bound states increases with the coupling constant. For the case of the symmetric dS brane and positive, there are NL(NL1) left chiral fermion bound states (including zero mode and massive KK modes) and NL −1 right chiral fermion bound states (including only massive KK modes).For the asymmetric dS brane scenario, the asymmetric factor a reduces the number of the bound fermion KK modes. For large enough a, there would not be any right chiral fermion bound mode, but at least one left chiral fermion zero mode.

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.

In this paper, we mainly investigate the WM2,s WL2,s system, in which the matter and the Liouville subsystems generate WM2,s and WL2,s algebras respectively. We first give a brief discussion of the physical states for corresponding W stings. The lower states are given by freezing the spin-2 and spin-s currents.Then, introducing two pairs of ghost-like fields, we give the realizations of W1,2,s algebras. Based on these linear realizations, BRST operators for W2,s algebras are obtained. Finally, we construct new BRST charges of Liouville system for WL2,s strings at the specific values of central charges c: c = −225/5 for WL2,3 algebra,c = −24 for WL2,4 algebra and c = −2,−286 /3 for WL2,6 algebra, at which the corresponding WL 2,s algebras are singular.

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).