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。特别对畴壁、涡旋、单极子和瞬子等孤子进行了研究。这些孤子被用作膜世界场景的背景孤子。我们主要研究了两个方面：1)研究超对称理论中的孤子。这些孤子在膜世界场景中的应用。我们主要研究作为非线性场微分方程解的孤子。我们研究了孤子动力学，打算将其应用于非微扰效应。我们已经在非线性sigma模型中计算出了八个增压器的畴壁解。我们研究了如何维持超对称的部分显化。此外，我们还得到了非阿贝尔规范理论中对于阿贝尔因子群具有Fayet-Iliopoulos项的超对称真空，以及对于超多重态具有非简并质量的超对称真空。利用这一结果，我们完整地计算出了非阿贝尔规范理论中的畴壁。发现这些域壁解的模空间是紧复格拉斯曼流形。在六维超对称非阿贝尔规范理论中也构造了涡旋。我们还研究了孤子上的有效拉格朗日量。在保留了1/4超对称性的孤子基础上，构造了非阿贝尔规范理论中域壁、涡旋和单极子的复合孤子。我们将畴壁结构造为带8个增压的规范理论的1/4 BPS解。这是理论中第一个具有八个增压的畴壁结的例子。我们也证明了块解彼此成任何角度都可以保持部分超对称。

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.