Yi-Shi Duan

Localization of matters on pure geometrical thick branes

In the literatures, several types of thick smooth brane configurations in a pure geometric Weyl integrable 5-dimensional space time have been presented. The Weyl geometry is a non-Riemannian modification of 5-dimensional Kaluza-Klein (KK) theory. All these thick brane solutions preserve 4-dimensional Poincare invariance, and some of them break Z2-symmetry along the extra dimension. In this paper, we study localization of various matter fields on these pure geometrical thick branes, which also localize the graviton. We present the shape of the potential of the corresponding Schrodinger problem and obtain the lowest KK mode. It is shown that, for both spin 0 scalars and spin 1 vectors, there exists a continuum gapless spectrum of KK states with m2 > 0. But only the massless mode of scalars is found to be normalizable on the brane. However, for the massless left or right chiral fermion localization, there must be some kind of Yukawa coupling. For a special coupling, there exist a series of discrete massive KK modes with m2 > 0. It is also showed that for a given coupling constant only one of the massless chiral modes is localized on the branes.

Bulk matters on symmetric and asymmetric de Sitter thick branes

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 Schrodinger 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 Poschl-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 ηΨ, there exists no mass gap but a continuous gapless spectrum of KK states. For the scalar-fermion coupling ηsin(/0)cos−δ(/0)Ψ with a positive coupling constant η, there exist some discrete bound KK modes and a series of continuous ones. The total number of bound states increases with the coupling constant η. For the case of the symmetric dS brane and positive η, there are NL(NL ≥ 1) 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.

Localization of fermions on a string-like defect

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.

The bifurcation theory of the Gauss-Bonnet-Chern topological current and Morse function

Abstract We detail the bifurcation of the GBC topological current and find different directions of the bifurcation. The GBC topological particles are found to split at the degenerate point of the field function φ, but the total charge of the GBC topological particles remains unchanged. Further, we find the GBC topological current of the gradient field of arbitrary function f bifurcating at its critical points until f evaluates into the Morse function; the topological charge of each topological particle is then ±1.

Topological structure of Gauss–Bonnet–Chern density and its topological current

The decomposition of spin connection on the sphere bundle of a compact and oriented even‐dimensional Riemannian manifold is detailed. It is shown that the Gauss–Bonnet–Chern form can be expressed in terms of a smooth vector fieldΦ and taken the form of the δ function δ(Φ). The topological current of the Gauss–Bonnet–Chern theorem and its topological structure are discussed.

Fermions in self-dual vortex background on a string-like defect

Abstract 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.

FERMIONIC ZERO MODES IN SELF-DUAL VORTEX BACKGROUND

We study fermionic zero modes in the background of self-dual vortex on a two-dimensional non-compact extra space in 5+1 dimensions. In the Abelian Higgs model, we present a unified description of the topological and non-topological self-dual vortex on the extra two dimensions. Based on it, we study the localization of bulk fermions on a brane with the inclusion of Yang–Mills and gravity backgrounds in six dimensions. Through two simple cases, it is shown that the vortex background contributes a phase shift to the fermionic zero mode, this phase is actually origin from the Aharonov–Bohm effect.

LOCALIZATION OF FERMIONIC FIELDS ON BRANEWORLDS WITH BULK TACHYON MATTER

Recently, Pal and Skar in Ref. 33 proposed a mechanism to arise the warped braneworld models from bulk tachyon matter, which are endowed with a thin brane and a thick brane. In this framework, we investigate localization of fermionic fields on these branes. As in the 1/2-spin case, the field can be localized on both the thin and thick branes with inclusion of scalar background. In the 3/2-spin extension, the general supergravity action coupled to chiral supermultiplets is considered to produce the localization on both the branes as a result.

Topological tensor current of p̃-branes in the φ-mapping theory

We present a new topological tensor current of p-branes by making use of the φ-mapping theory. It is shown that the current is identically conserved and behaves as δ(φ), and every isolated zero of the vector field φ(x) corresponds to a “magnetic” p-brane. Using this topological current, the generalized Nambu action for multi p-branes is given, and the field strength F corresponding to this topological tensor current is obtained. It is also shown that the magnetic charges carried by p-branes are topologically quantized and labeled by Hopf index and Brouwer degree, the winding number of the φ mapping.

The Origin and Bifurcation of the Space-Time Defects in the Early Universe

In the early universe, a new topological invariant is interpreted as the space-time dislocation flux and is quantized in the topological level. By extending to a topological current of dislocations, the dynamic form of the defects is obtained under the condition that the Jacobian determinant D(φ/u) ≠ 0. When D(φ/u) = 0, it is shown that there exists the crucial case of branch process. Based on the implicit function theorem and the Taylor expansion, the origin and bifurcation of the space-time dislocations are detailed in the neighborhoods of the limit points and bifurcation points of φ-mapping, respectively. It is pointed out that, since the dislocation current is identically conserved, the total topological quantum numbers of the branched dislocation fluxes will remain constant during their origin and bifurcation processes, which are important in the early universe because of spontaneous symmetry breaking.