N=4 SYM中的负反常维数
Negative anomalous dimensions in N=4 SYM
摘要：
我们阐明了在有限$N_c$的$\mathcal{N}=4\ SU(N_c)$ SYM中的$so(6)$ -单线多迹算子的单圈反常维数。首先，我们研究了$1/N_c$校正如何提升谱的大$N_c$简并度，我们称之为算子次混合问题。我们观察到所有大的$N_c$零模从$1/N_c^2$阶开始获得非正的反常维数，并且它们只在前导阶具有相同迹数的算子之间混合。其次，我们研究了长度等于$2N_c$的算子的最低单圈维数。随着$N_c$的增加，这种算子的维数变得更负，最终将以双标度极限发散。第三，我们从幺正性的角度研究了有限$N_c$上的能级交叉结构。最后，我们找到了大$N_c$零模与Mandelivery变量的完全对称多项式之间的对应关系。
英文摘要：
We elucidate aspects of the one-loop anomalous dimension of $so(6)$-singlet multi-trace operators in $\mathcal{N}=4\ SU(N_c)$ SYM at finite $N_c$. First, we study how $1/N_c$ corrections lift the large $N_c$ degeneracy of the spectrum, which we call the operator submixing problem. We observe that all large $N_c$ zero modes acquire non-positive anomalous dimension starting at order $1/N_c^2$, and they mix only among the operators with the same number of traces at leading order. Second, we study the lowest one-loop dimension of operators of length equal to $2N_c$. The dimension of such operators becomes more negative as $N_c$ increases, which will eventually diverge in a double scaling limit. Third, we examine the structure of level-crossing at finite $N_c$ in view of unitarity. Finally we find out a correspondence between the large $N_c$ zero modes and completely symmetric polynomials of Mandelstam variables.
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