R_b and R_l in MSSM without R-Parity

We examined Z\ell^+\ell^- and Zb\bar b couplings in the minimal supersymmetric model (MSSM) with explicit R-parity violating interactions. We found the top quark L-violating couplings \lambda'_{i3k} and B-violating couplings \lambda''_{3j3} could give significant contributions through the top quark loops. To accomadate the latest R_{\ell} data, \lambda'_{i3k} are suject to stringent bounds, some of which can be much stronger than the current bounds. Within the current perturbative unitarity bound of 1.25 for \lambda''_{3j3}, the R_b value in R-violating MSSM agrees well with the experimental data at $2\sigma$ level, but may lie outside the 1\sigma range depending on the involved sfermion mass.Comment: results update

Holographic Wilsonian RG Flow and Sliding Membrane Paradigm

We study the relations between two different approaches to the holographic Renormalization Group (RG) flow at the dual gravity level: One is the radial evolution of the classical equation of motion and the other is the flow equation given by the holographic Wilsonian RG coming from the cut off independence. Apparently, the two flows look different. We give general proofs that the two flows are actually equivalent. The role of the momentum continuity (MC) is essential. We show that MC together with cutoff independence gives the evolution equation of the boundary values. Equivalence of conductivity flows in two paradigm has been shown as an explicit example. We also get the connecting formula of Green functions and AC conductivity at arbitrary slice in terms of its value at horizon for various geometry backgrounds.Comment: 21pages, 9 figures, published version, minor change