Modern Physics Letters A

In between the 80's and 90's we witnessed deep interactions between mathematics and theoretical physics, especially in the understanding of low-dimensional topology in terms of quantum field theory. For example, Jones polynomials (Chern–Simons–Witten theory), Donaldson and Seiberg–Witten invariants (SUSY Yang–Mills theory) and mirror symmetry (T duality in strings) are all naturally understood in terms of QFT and strings. Recent developments indicate a close relationship between gauge theory and gravity theory both in physics and in low-dimensional topology. We shall survey these developments and report some of our work. We shall also find that the keys to connect geometric and physical objects are through symmetry and quantization.

We present an overview of the ways in which D-brane charges are classified in terms of K-theory, emphasizing the natural physical interpretations of a homological classification within a topological setting.

Short-distance expansion of the total semileptonic B widths is reviewed for the OPE-conformable scheme employing low-scale running quark masses. The third- and fourth-order BLM corrections are given and the complete resummation of the BLM series presented. The effect of higher perturbative orders with running quark masses is found to be very small. Numerical consequences for |V_cb| are addressed.

We evaluate the compositeness effects of tau lepton on the vertex Wτν_τ in the context of an effective Lagrangian approach. We consider that only the third family is composed and we get the corrections to the non-universal lepton coupling g_τ/g_e. As the experimental bounds on non-universal lepton couplings in W decays are weak, we find that the contributions of the excited particles do not give realistic limits on the excited mass, since they lead to Λ < m*.

We present a class of solutions for a heat conducting fluid sphere, which radiates energy during collapse without the appearance of horizon at the boundary at any stage of the collapse. A simple model shows that there is no accumulation of energy due to collapse since it radiates out at the same rate as it is being generated.

We discuss the decoupling solution to SUSY flavor problem in the fat brane scenario. We present a simple model to yield the decoupling sfermion spectrum in a five-dimensional theory. Sfermion masses are generated by the overlap between the wave functions of the matter fields and the chiral superfields on the SUSY breaking brane. Two explicit examples of the spectrum are given.

We calculate the contributions of the neutral top-pion to the process in the framework of topcolor-assisted technicolor (TC2) models. Our results show that can give significant contributions to this process. With reasonable values of the parameters in TC2 models, the cross-section σ can reach 1.3 pb which may be detected at the eγ collisions based on the future high energy linear e⁺e^- collider experiments.