Induced Field Theory on the Brane World

我们得到了关于膜世界或一般场论的诱导场论的以下新结果。(1)用量子理论的方法推导了高维孤子局域化的膜世界中几何物体、孤子涨落和被困物体的场论。(2)在非阿贝尔规范理论中，规范场是复合的（即诱导场理论），只有当存在足够多的费米子种时，才有可能违反渐近自由。诱导场理论中的复合场耦合常数是精确尺度不变的。(3)在假设自然的情况下，我们推导出了由新物理学产生的费米子偶极矩的一般界限，并将其应用于观测结果。(4)将三维非线性σ模型推广到非交换场论中，得到了关于孤子解的结构、模的性质和孤子的低能量散射的几个新结果。(5)分别在四维和二维非反交换超空间上构造了CP(n)非线性sigma模型。(6)研究了SU(3) x SU(3) x U(1)模型的现象学性质。(7)重新考虑了随机场Ising模型的降维问题。(8)给定多个边缘耦合常数的双环beta函数，导出了驱动到红外不动点的运行耦合常数的渐近公式。

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.