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。特别研究了磁区壁、涡旋、单极子和瞬子等孤子。我们主要研究了两个方面：i)研究超对称理论中的孤子；ii)这些孤子在薄膜世界中的应用。我们主要研究孤子作为场的非线性微分方程解的问题。我们研究了孤子动力学，并将其应用于非微扰效应，得到了具有8个超荷的非线性sigma模型中的磁区壁解。我们研究了如何保持部分超对称性，得到了非阿贝尔规范理论中具有阿贝尔因子群的Fayet-Iliopoulos项和超多重群的非简并质量的超对称真空。利用这一结果，我们已经完全计算出非阿贝伦规范理论中的域壁。这些区域壁解的模空间是紧致的复Grassmann流形，并在六维超对称非阿贝尔规范理论中构造了涡量。作为保留1/4超对称性的孤子，我们构造了非阿贝伦规范理论中的磁区壁、涡旋和单极子的复合孤子，并将磁区壁结构造为具有8个超电荷的规范理论的1/4 BPS解。这是具有八个超荷的理论中的第一个磁区壁结的例子。我们还证明了相互成任意角度的集总解可以保持部分超对称性。

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.