Vortices In Quantum R(?)ntgen Effect And Chiral-Antichiral Scalar Propagator In â…¡B Supergravity Coset Superspace

This thesis is comprised of the research work in topological quantum field theory and superstring theory. In the topological quantum field theory part, the vortices in quantum Rontgen effect are studied in light of Duan's topological current theory. In the superstring theory part, the chiral-antichiral scalar propagator in type IIB supergravity is obtained by means of coset superspace approach.●In the topological quantum field theory part, the vortices in quantum Rontgen effect in BEC are throughly studied in light of Duan's topological current theory. First of all, the explicit expression of the curl of the vortices velocity field is given, where the functionδ(φ) implies that the vortices can only occur at the zero points of the wave functionφ. The expansion ofδ(φ) at the regular zero points ofφis obtained, which reveals the inner topological structure of the vortex lines, and shows that it is related to the Hopf indicesβi and Brouwer degreesηi of the 0-mapping. Correspondingly, the explicit expression of the magnetic field is given. This magnetic field behaves like the one generated by monopoles located at the vortex lines, and the magnetic flux is quantized. Secondly, the vortex lines generate, annihilate, split, merge or intersect at the critical zero points ofφ. All these situations are discussed in detail. Lastly, the reduced dynamic equation is derived, from which the conserved dynamic quantity on the stable vortex lines is obtained.●In the superstring theory part, the chiral-antichiral scalar propagator in typeⅡB super-gravity of the AdS/CFT correspondence is obtained. First of all, for the nonsuper case, the scalar propagator in the maximal bosonic subspace AdS5×S5 of typeⅡB super-gravity is derived via Weyl scale transformation. Its Kaluza-Klein expansion over S5 is obtained. The spherical harmonics are Gegenbauer polynomials and the component fields are the Gegenbauer functions of the second kind. Secondly, for the super case, the coset superspace of superconformal group SU(2,2│4) is constructed. The chiral-antichiral scalar propagator in type IIB supergravity is derived in this coset superspace. It is verified that this propagator satisfies the Green equation and theκ-symmetry rela-tion. Setting the fermionic variables to zero, it can be reduced to the scalar propagator in the nonsuper case, which shows the results are consistent.This thesis is organized as follows:●In chapter 1, Duan's topological current theory and gauge potential decomposition the-ory are concisely reviewed.●In chapter 2, supersymmetry, super Yang-Mills theory, supergravity, and the AdS/CFT correspondence are concisely reviewed.●In chapter 3, the vortices in quantum Rontgen effect are studied in light of Duan's topological current theory.●In chapter 4, the scalar propagator in AdS5 x S5 is studied at the nonsuper case. While for the super case, the chiral-antichiral scalar propagator is studied in the coset super-space of the superconformal group SU(2,2|4).●In chapter 5, the main results of this thesis are summarized, and further research work is proposed.