论文标题
格拉曼尼亚式的固定模型和较高的自旋电流
The Grassmannian-like Coset Model and the Higher Spin Currents
论文作者
论文摘要
在类似Grassmannian的coset型号中，$ \ frac {su（n+m）_k} {su（n）_k \ times u（1）_ {k n m（n+m）}} $，Creutzig和Hikida发现了被控的Spin- Spin- spin- spin- $ 2,3 $ currents and the Nutral currents and Nutral spin- and $ 2,3 $ 2,3 $ 2,3 $ corrents。在本文中，作为十年前的Gaberdiel-Gopakumar猜想的扩展，我们计算了运营商的产品扩展（OPE），在充电的旋转率为-2美元的电流和本身之间，充电的Spin-2 $当前的OPE与电荷$ 2 $的电流与$ 3 $的电流和OPE之间的ope和ope之间的ope和ope之间的ope和ope ope and ope and ope and ope and ope and op ope and op ope and op ope and op the neutial spin- $ 3 $ $ 3 $ $ $ $ $ $ n $ n $ n，m $ n $ k $ $ n $ n，m，m，m，m。从第二操作中，我们获得了新的带电的准主要旋转 - $ 4 $当前，而从最后一个开始，新的中性初级旋转 - $ 4 $当前的电流是隐式发现的。 OPES结构常数的无限限制在$ M \ times m $矩阵概括的渐近对称性中描述了$ ads_3 $较高的旋转理论。此外，已充电的旋转$ 3 $当前和本身之间的操作是针对固定$（n，m）=（5,4）$的，任意$ k $，最高为三阶杆。我们还获得了电荷旋转$ 1,2,3 $电流与中性旋转$ 3 $当前之间的选择。从最后的操作中，我们意识到存在上述带电的准主要自旋的存在-4 $ 4 $当前的二阶Pole中的固定$（n，m）=（5,4）$。我们评论复杂的免费费米昂实现。
In the Grassmannian-like coset model, $\frac{SU(N+M)_k}{SU(N)_k \times U(1)_{k N M (N+M)}}$, Creutzig and Hikida have found the charged spin-$2,3$ currents and the neutral spin-$2,3$ currents previously. In this paper, as an extension of Gaberdiel-Gopakumar conjecture found ten years ago, we calculate the operator product expansion (OPE) between the charged spin-$2$ current and itself, the OPE between the charged spin-$2$ current and the charged spin-$3$ current and the OPE between the neutral spin-$3$ current and itself for generic $N, M$ and $k$. From the second OPE, we obtain the new charged quasi primary spin-$4$ current while from the last one, the new neutral primary spin-$4$ current is found implicitly. The infinity limit of $k$ in the structure constants of the OPEs is described in the context of asymptotic symmetry of $M \times M$ matrix generalization of $AdS_3$ higher spin theory. Moreover, the OPE between the charged spin-$3$ current and itself is determined for fixed $(N,M)=(5,4)$ with arbitrary $k$ up to the third order pole. We also obtain the OPEs between charged spin-$1,2,3$ currents and neutral spin-$3$ current. From the last OPE, we realize that there exists the presence of the above charged quasi primary spin-$4$ current in the second order pole for fixed $(N,M)=(5,4)$. We comment on the complex free fermion realization.
