New mechanisms of breakdown of translational invariance and the phase transition

均匀磁场中n维环面上的量子力学研究了均匀磁场中n维环面上的量子力学系统。经典地，环面的平移不变性不会被打破。然而，我们已经证明，量子力学的连续平移不变性被打破，并减少到一些离散移位对称。具有点奇点的一维量子力学中的超对称性点奇点的存在打破了平移不变性。我们发现这个系统有很多有趣的特性。特别地，我们证明了系统可以具有任意数量的超荷的扩展超对称。这项工作导致了一种解决规范层次问题的新机制的发现。高维规范理论中的隐藏超对称我们证明了任何具有紧致额外维的高维规范理论在一般的四维谱中都具有隐藏的N=2超对称结构。大质量层次的无希格斯规范对称破缺我们提出了一种新的解决规范层次问题的机制。我们从高维规范理论开始。如上所示，该理论具有一个隐藏的N=2超对称。为了非摄动破缺它，证明了规范对称可以用指数级小的破缺质量尺度破缺，从而得到规范层次问题的解。

Quantum mechanics on the n-dimensional torus in the uniform magnetic fieldWe studied the quantum mechanical system on the n-dimensional torus in the uniform magnetic field. Classically, the translational invariance of the torus is not broken. We have, however, shown that quantum-mechanically the continuous translational invariance is broken and reduces to some discrete shift symmetry.Supersymmetry in the one-dimensional quantum mechanics with point singularitiesThe existence of point singularities breaks the translational invariance. We have found that the system has a variety of interesting features. Especially, we have shown that the system can possess extended supersymmetry with an arbitrary large number of supercharges. This work leads to the discovery of a new mechanism of solutions to the gauge hierarchy problem.Hidden supersymmetry in higher dimensional gauge theoriesWe have proved that any higher dimensional gauge theories with compact extra dimensions possess hidden N=2 supersymmetric structure in the 4-d spectrum in general.Higgsless gauge symmetry breaking with large mass hierarchyWe proposed a new mechanism of solutions to the gauge hierarchy problem. We start with a higher dimensional gauge theory. As was shown in the above work, the theory possesses a hidden N=2 supersymmetry. To break it non-perturbatively, it is shown that the gauge symmetry can be broken with an exponentially small breaking mass scale, which leads to a solution to the gauge hierarchy problem.