论文标题
不可变动的时间转换对称性
Non-invertible Time-reversal Symmetry
论文作者
论文摘要
在量规理论中，通常指出的是，时间逆转对称性仅存在$θ= 0 $或$π$，对于$2π$ - 周期性$θ$ - 角。在本文中，我们指出的是，在免费的麦克斯韦理论和大规模QED中，每个有理$θ$ - 角，即$θ=πp/n $，都有不可粘的时间反转对称性。不可逆转的时间转换对称性是由无逆的保守的反线运算符实现的。它是天真的时间反转转换和分数量子霍尔状态的组成。我们还发现在非亚洲仪表理论中类似的不可逆转的时间反转对称性，包括$ \ MATHCAL {n} = 4 $ $ su（2）$沿着位点$ |τ|τ| = 1 $在共同性上。
In gauge theory, it is commonly stated that time-reversal symmetry only exists at $θ=0$ or $π$ for a $2π$-periodic $θ$-angle. In this paper, we point out that in both the free Maxwell theory and massive QED, there is a non-invertible time-reversal symmetry at every rational $θ$-angle, i.e., $θ= πp/N$. The non-invertible time-reversal symmetry is implemented by a conserved, anti-linear operator without an inverse. It is a composition of the naive time-reversal transformation and a fractional quantum Hall state. We also find similar non-invertible time-reversal symmetries in non-Abelian gauge theories, including the $\mathcal{N}=4$ $SU(2)$ super Yang-Mills theory along the locus $|τ|=1$ on the conformal manifold.
