Abstract
In this thesis, we study some special topics in particle physics . One is about the R-parity breaking sector in the minimal supersymmetric standard model (MSSM) . We give a detail study in the R-parity breaking sector including both trilinear and bilinear breaking terms within the single VEV convention . We show that neutrinoless double beta decay can give rise to strong constraints on the quadratic interaction $\mu_i$ that break both lepton number and R parity in supersymmetric theories . We demonstrate that the R-parity breaking interactions within their current experimental upper bounds can give rise to large CP asymmetry in radiative B decays that may be detectable in the upcoming B factories . We calculate the dominant two loop contributions to the the muon (g-2) due to the exotic Higgs boson sector that exists in most extensions of the Standard Model . The leading effects comes from diagrams of the Barr-Zee type . We show that the pseudoscalar Higgs boson can give rise to contribution as large as the electroweak contributions that are measureable in the next round of (g-2) experiment . We also calculate the scalar Higgs contribution which is roughly one order of magnitude smaller . By expanding the method of deconfinement, we present new dual descriptions for an ${\cal N}&=1 SUSY SU(N) gauge theory with matter in anti-symmetric tensor, fundamental, and anti-fundamental representations . The idea of generalized method of deconfinement is that one can not only treat the rank-two tensor but also the quarks in the fundamental representation as bound states of another auxiliary gauge group . We also give some applications in the chiral-nonchiral dual pairs .