论文标题
Chern-Simons-Marts理论的线路运算符和三个维度的琼脂化
Line Operators in Chern-Simons-Matter Theories and Bosonization in Three Dimensions
论文作者
论文摘要
我们在基本代表中研究了与玻色粒或费米斯物质的Chern-Simons理论。这些理论中最基本的操作员是中间线运算符，最简单的例子是威尔逊线以基本面结尾。我们沿任意平滑路径以及在有限的thooft耦合处对共形线运算符以及保形尺寸和边界运算符的横向旋转的光谱进行了分类。这些线算子被证明满足一阶手性进化方程，其中两个线路运算符的分解产物给出了路径的平滑变化。我们认为，该方程与边界运营商的光谱足以唯一确定这些运算符的期望值。我们通过在直线上引导位移操作员的两点函数来证明这一点。我们表明，玻色子理论中的线算子和费米子理论满足相同的进化方程，并具有相同的边界操作范围。
We study Chern-Simons theories at large $N$ with either bosonic or fermionic matter in the fundamental representation. The most fundamental operators in these theories are mesonic line operators, the simplest example being Wilson lines ending on fundamentals. We classify the conformal line operators along an arbitrary smooth path as well as the spectrum of conformal dimensions and transverse spins of their boundary operators at finite 't Hooft coupling. These line operators are shown to satisfy first-order chiral evolution equations, in which a smooth variation of the path is given by a factorized product of two line operators. We argue that this equation together with the spectrum of boundary operators are sufficient to uniquely determine the expectation values of these operators. We demonstrate this by bootstrapping the two-point function of the displacement operator on a straight line. We show that the line operators in the theory of bosons and the theory of fermions satisfy the same evolution equation and have the same spectrum of boundary operators.
