Induced Field Theory on the Brane World

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We obtained the following new results about induce field theory on the brane world or field theories in general. (1)We derived, in a quantum theoretical way, field theories for the geometrical objects, solitonic fluctuations, and trapped objects on the brane worlds, which is localized by higher dimensional soliton. (2)In the non-abelian gauge theories, gauge fields can be composite (i. e. induced field theory) only if there exist so many fermion species as the asymptotic freedom is violated. The composite field coupling constants in the induced field theories are exactly scale invariant. (3)Assuming naturalness, we derived general bounds on the fermion-dipole moments arising from new physics and applied them to the observed results. (4)We extended the three dimensional non-linear sigma model to the non-commutative field theory, and obtained several new results on structure of the solitonic solutions, properties of the moduli, and low energy scattering of the solitons. (5)We successfully constructed CP(n) nonlinear sigma model on non-anti-commutative super spaces in four dimensions and in two dimensions. (6)We investigated phenomenological properties of the SU(3) x SU(3) x U(1) model. (7)The dimensional reduction is reconsidered for the random-field Ising model. (8)Given a two-loop beta function for multiple marginal coupling constants, we derived an asymptotic formula for the running coupling constants driven to an infrared fixed point.