论文标题
三维的Chern-Simons理论什么时候有时间逆转对称性？
When Does A Three-Dimensional Chern-Simons-Witten Theory Have A Time Reversal Symmetry?
论文作者
论文摘要
在本文中，我们完全表征了与圆环仪表组的时间逆转三维Chern-Simons仪表理论。在拉格朗日的层面上，托拉尔·雪恩·塞蒙斯理论是由整体晶格定义的，而在量子级别，它完全取决于有限的阿贝尔群体上的二次功能和一个整数mod 24。我们发现，量子时间交流的理论可以由经典的lagrangians定义为综合的lagrangians，从而由整合的lagrangians定义，该理论是在构成的，该理论已被定义为一个自动化的latterices，这些理论可以自我构成，该理论可以自以为是的，该理论可以自以为是的，这些理论可以自以为是的，这些理论可以自以为是的，该理论可以自以为是的，该理论可以自以为是的，该理论可以自以为是的，该理论可以自以为是的一定的latteric latteric lattect an格子。我们发现，量子Chern-simons理论承认，相关模块化张量类别的较高高斯总和是真实的。我们猜想较高的高斯总和的现实是必需的，足以使一般的非亚伯式Chern-Simons接收量子T-对称性。
In this paper, we completely characterize time-reversal invariant three-dimensional Chern-Simons gauge theories with torus gauge group. At the level of the Lagrangian, toral Chern-Simons theory is defined by an integral lattice, while at the quantum level, it is entirely determined by a quadratic function on a finite Abelian group and an integer mod 24. We find that quantum time-reversally symmetric theories can be defined by classical Lagrangians defined by integral lattices which have self-perpendicular embeddings into a unimodular lattice. We find that the quantum toral Chern-Simons theory admits a time-reversal symmetry iff the higher Gauss sums of the associated modular tensor category are real. We conjecture that the reality of the higher Gauss sums is necessary and sufficient for a general non-Abelian Chern-Simons to admit quantum T-symmetry.
