Study of supersymmetric non-linear sigma models

研究非线性西格玛模型很重要，原因有几个。二维非线性Sigma模型描述了弦在弯曲时空中的传播。它也是一个非微扰研究场论中的困难现象的体育馆，如质量产生、束缚态问题、动力学对称破缺。它还提供了一个在微扰理论中不可重整化的可能的可重整化场论的例子。在这个项目中，我们提出了具有N=2超对称的非线性sigma模型的辅助场形式。B)利用上述方法研究了N=2超对称非线性sigma模型的非微扰性质。C)利用重整化群方程寻找共形场理论。D)研究了非紧流形上的共形不变非线性sigma模型。通过引入D项和F项约束，我们成功地建立了厄米对称空间上的N=2超对称非线性sigma模型。我们用大N方法研究了Cp^N和Q^N上的非线性Sigma模型中的非微扰现象，得到了非紧致Ricci平坦流形上的共形场论。我们推导了N=2超对称非线性Sigma模型的非微扰重整化群方程。通过解不动点方程，我们发现了新的反常维共形场理论。

Study of non-linear sigma models is important for several reasons. Two-dimensional non-linear sigma models describe propagation of strings in vurved space-time. It is also a gymnasium for non-perturbative study of difficult phenomena in field theories, like mass generation, bound states problem, dynamical symmetry breaking. It also offers an example of a possible renormalizable field theory that is not renormalizable in perturbation theory. In this project, we proposedA)Auxiliary field formulation of non-linear sigma models with N=2 supersymmetry.B)Non-perturbative study of N=2 supersymmetric non-linear sigma models by using the above methodC)Search of conformal field theories by using the renormalization group equation.D)Study of conformally invariant non-linear sigma models on non-compact manifolds.We successfully formulated N=2 supersymmetric non-linear sigma models on hermitian symmetric spaces by introducing both D-term and F-term constraints. We applied the large N method to study the non-perturbative phenomena in non-linear sigma models on CP^N and Q^N. We also obtained conformal field theories on non-compact Ricci-flat manifolds constructed as a line bundle Einstein-Kahler manifold. We derived the non-perturbative renormalization group equation for N=2 supersymmetric non-linear sigma models. By solving the fixed point equation, we found new conformal field theories with anomalous dimension.