论文标题
Matter Chern-Simons理论的交叉对称性在有限的$ n $和$ k $
Crossing Symmetry in Matter Chern-Simons Theories at finite $N$ and $k$
论文作者
论文摘要
我们提出了Chern-Simons仪表理论的交叉对称规则的猜想，该规则与大量物质相互作用，价格为2美元+1 $。我们的交叉规则是根据威尔逊线的特定缠结的期望值给出的，并将其减少到大型Chern-Simons级别的标准规则。我们为两个基本插入的特殊情况提供了完全明确的结果。这些公式与这些理论之间的猜想级级，bose-fermi二元性一致，并采用$ q = e^{\ frac {\ frac {2πi}κ} $的大型$ k $对应物的变形。在't Hooft大$ n $中，我们的结果限制了我们的结果以一种转折为标准规则：$ s $ -matrix的$ \ frac {\ frac {\sinπλ} {πλ} $（其中$λ$是't HOOFT coupling），从而解释了“ Anomalous” crossing properties of night cross $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $ n $。
We present a conjecture for the crossing symmetry rules for Chern-Simons gauge theories interacting with massive matter in $2+1$ dimensions. Our crossing rules are given in terms of the expectation values of particular tangles of Wilson lines, and reduce to the standard rules at large Chern-Simons level. We present completely explicit results for the special case of two fundamental and two antifundamental insertions in $SU(N)_k$ and $U(N)_k$ theories. These formulae are consistent with the conjectured level-rank, Bose-Fermi duality between these theories and take the form of a $q=e^{\frac{ 2 πi }κ}$ deformation of their large $k$ counterparts. In the 't Hooft large $N$ limit our results reduce to standard rules with one twist: the $S$-matrix in the singlet channel is reduced by the factor $\frac{\sin πλ}{πλ} $ (where $λ$ is the 't Hooft coupling), explaining `anomalous' crossing properties observed in earlier direct large $N$ computations.
