Models with extra dimensions and supersymmetry

我们用超对称理论研究了具有额外维度的统一模型。特别是孤立子，如畴壁，旋涡，单极子和瞬子进行了研究。我们主要研究了两个方面：一是在超对称理论中研究孤立子，二是孤立子在膜世界中的应用，主要研究了孤立子作为非线性场微分方程解的情况。本文研究了孤子动力学在非微扰效应中的应用，给出了具有八个超荷的非线性σ模型的畴壁解。研究了如何保持部分超对称性的显现，进而得到了非阿贝尔规范理论中的超对称真空，阿贝尔因子群具有Fayet-Iliopoulos项，超多重态具有非简并质量.利用这一结果，我们完整地计算了非Abelain规范理论中的畴壁。这些畴壁解的模空间是紧致的复Grassmann流形，在六维超对称非阿贝尔规范理论中也构造了涡旋。我们还研究了孤子的有效拉格朗日量，在保持1/4超对称性的情况下，构造了非Abelain规范理论中的畴壁、涡旋和单极子的复合孤子，构造了八超荷规范理论的畴壁结1/4 BPS解。这是八个超荷理论中第一个畴壁结的例子，我们还证明了相互成任意角度的集总解都能保持部分超对称性。

We have studied unified models with extra dimensions using supersymmetric theories. In particular, solitons such as domain walls, vortices, monopoles and instantons are studied. These solitons are intended to be used as background solitons for the brane-world scenario.We have studied mainly two aspects :I)studying solitons in supersymetric theories.II)Application of these solitons to brane-world scenario.We have focused on studying solitons as solutions of nonlinear differential equations for fields. We have studied soliton dynamics intending an application to nonperturbative effects.We have worked out domain wall solutions in nonlinear sigma models with eight supercharges. We have studied how to maintain part of supersymmetry manifest.Moerover, we obtained supersymmetric vacua in non Abelian gauge theories with Fayet-Iliopoulos term for Abelian factor group, and with nondegenerate masses for hypermultiplets. Using this result, we have worked out domain walls in nonAbelain gauge theories completely. Moduli space of these domain wall solutions is found to be compact complex Grassmann manifold.Vortices are also constructed in supersymmetric nonAbelian gauge theories in six dimensions. We also studied the effective Lagrangian on the soliton.As solitons with 1/4 of supersymmetry preserved, we constructed composite solitons of domain walls, vortices and monopoles in nonAbelain gauge theories.We have constructed domain wall junction as 1/4 BPS solution of gauge theories with eight supercharges. This is the first example of domain wall junction in theories with eight supercharges.We have also shown that lump solutions making any angle with each other can preserve part of supersymmetry.