We report on an attempt to solve the gauge hierarchy problem in the framework of higher dimensional gauge theories. Both classical Higgs mass and quadratically divergent quantum correction to the mass are argued to vanish. Hence the hierarchy problem in its original sense is solved. The remaining finite mass correction is shown to depend crucially on the choice of boundary condition for matter fields, and a way to fix it dynamically is presented. We also point out that on the simply-connected space S 2 even the finite mass correction vanishes. *

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We present a detailed study of B → K 1 (1270)γ and B → K 1 (1400)γ decays. Using the light-cone sum rule technique, we calculate the B → K 1A (1 3 P 1 ) and B → K 1B (1 1 P 1 ) tensor form factors, T K 1A

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We explore the phase structure and symmetry breaking in four-dimensional SU(3) gauge theory with one spatial compact dimension on the lattice ($16^3 \times 4$ lattice) in the presence of fermions in the adjoint representation with periodic boundary conditions. We estimate numerically the density plots of the Polyakov loop eigenvalues phases, which reflect the location of minima of the effective potential in the Hosotani mechanism. We find strong indication that the four phases found on the lattice correspond to SU(3)-confined, SU(3)-deconfined, SU(2) x U(1), and U(1) x U(1) phases predicted by the one-loop perturbative calculation. The case with fermions in the fundamental representation with general boundary conditions, equivalent to the case of imaginary chemical potentials, is also found to support the $Z_3$ symmetry breaking in the effective potential analysis.Comment: 43 pages, 19 figures, 3 tables. Updated version matches the journal conten