Topological Solitons in Field Theory

研究了超对称规范理论中BPS非阿贝尔涡模空间度规的渐近形式，并对重合涡模空间进行了分类。我还推广了涡旋规范群。我构造了非阿贝尔涡及其内模的解和这些模的有效场理论，计算了两个涡旋之间的相互作用，并导出了一个涡旋与胶子和声子的相互作用。构造了费米子零模，研究了涡旋的交换统计性质。此外，我还构造了多组分玻色-爱因斯坦凝聚体中的非阿贝尔涡、磁区壁(D膜)和纽结孤子。

I have studied the asymptotic form of the moduli space metric for BPS non-Abelian vortices in supersymmetric gauge theories, and have classified moduli space for coincident vortices. I have also generalized gauge groups of vortices. I have constructed solutions of non-Abelian vortices, their internal moduli and the effective field theory for those moduli, calculated the interaction between two vortices, and derived the interaction of a vortex with gluons and phonons. I have also constructed the fermion zero mode and investigated the exchange statistics of vortices. Moreover I have constructed non-Abelian vortices, domain walls (D-branes) and knot solitons in multi-component Bose-Einstein condensates.