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arXiv 1701.02410hep-th
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正交陪集理论中的高自旋流

Higher Spin Currents in the Orthogonal Coset Theory

Changhyun Ahn

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96 pages
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摘要：

在陪集模型$(D_N^{(1)} \oplus D_N^{(1)},D_N^{(1)})$中，在能级$(k_1,k_2)$处，得到了包含四次WZW电流的高自旋$4$电流，该电流与秩为$4$的完全对称的$SO(2N)$不变量$d$张量收缩.对于任意有限的$N$和具有$k_1=1$的$k_2$，得到了具有两个标量的三点函数。它们也在大$N$ 't Hooft极限中确定。当其中一个能级是$SO(2N)$的对偶Coxeter数$k_1=2N-2$时，由${\cal N}=1$超共形代数中的自旋$\frac{3}{2}$流与上述高自旋$4$流之间的算符乘积展开（OPE）得到高自旋$\frac{7}{2}$流，它包含与上述$d$张量收缩的分裂伴随费米子和结构常数的三重乘积.描述了较高自旋$\frac{7}{2}, 4$电流之间的OPEs。对于$k_1=k_2=2N-2$，当两个能级都等于$SO(2N)$的对偶Coxeter数时，得到了$U(1)$电荷$\frac{4}{3}$的高自旋$3$流，它包含了自旋$\frac{1}{2}$（2）的伴随费米子与$d$张量和两个结构常数的乘积收缩的6个乘积.相应的${\cal N}=2$高自旋多重态是通过计算剩余的高自旋$\frac{7}{2}, \frac{7}{2}, 4$电流，借助于${\cal N}=2$超共形代数中的两个自旋$\frac{3}{2}$电流来确定的。得到另一个${\cal N}=2$高自旋多重态，其$U(1)$电荷与上述${\cal N}=2$高自旋多重态之一相反。本文还讨论了这两种${\cal N}=2$高自旋多重态之间的OPE。

英文摘要：

In the coset model $(D_N^{(1)} \oplus D_N^{(1)},D_N^{(1)})$ at levels $(k_1,k_2)$, the higher spin $4$ current that contains the quartic WZW currents contracted with completely symmetric $SO(2N)$ invariant $d$ tensor of rank $4$ is obtained. The three-point functions with two scalars are obtained for any finite $N$ and $k_2$ with $k_1=1$. They are determined also in the large $N$ 't Hooft limit. When one of the levels is the dual Coxeter number of $SO(2N)$, $k_1=2N-2$, the higher spin $\frac{7}{2}$ current, which contains the septic adjoint fermions contracted with the above $d$ tensor and the triple product of structure constants, is obtained from the operator product expansion (OPE) between the spin $\frac{3}{2}$ current living in the ${\cal N}=1$ superconformal algebra and the above higher spin $4$ current. The OPEs between the higher spin $\frac{7}{2}, 4$ currents are described. For $k_1=k_2=2N-2$ where both levels are equal to the dual Coxeter number of $SO(2N)$, the higher spin $3$ current of $U(1)$ charge $\frac{4}{3}$, which contains the six product of spin $\frac{1}{2}$ (two) adjoint fermions contracted with the product of $d$ tensor and two structure constants, is obtained. The corresponding ${\cal N}=2$ higher spin multiplet is determined by calculating the remaining higher spin $\frac{7}{2}, \frac{7}{2}, 4$ currents with the help of two spin $\frac{3}{2}$ currents in the ${\cal N}=2$ superconformal algebra. The other ${\cal N}=2$ higher spin multiplet, whose $U(1)$ charge is opposite to the one of above ${\cal N}=2$ higher spin multiplet, is obtained. The OPE between these two ${\cal N}=2$ higher spin mutiplets is also discussed.

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