论文标题
在关键$ o（n）$型号的大型电荷领域
On the Large Charge Sector in the Critical $O(N)$ Model at Large $N$
论文作者
论文摘要
我们以排名为$ o（n）$的$ o（n）$在任意尺寸$ d $中的$ o（n）$的对称的运营商在$ n $的限制和大型费用$ j $的限制中，带有$ j/n \ equiv \ equiv \ hat {j} $固定。在此限制下，操作员的缩放尺寸可以通过半经典的鞍点计算获得。使用大致$ n $的关键$ o（n）$模型的标准Hubbard-stratonovich描述，我们解决了相关的鞍点方程，并确定缩放维度作为$ d $和$ \ hat {J j} $的函数，找到所有现有结果的协议。在$ 4 <d <6 $中，我们观察到，大电荷运营商的缩放维度在比率$ j/n $的临界值之上变得复杂，这表明该理论在该范围内的不稳定性。最后，我们还得出了涉及两个“重”和一个或两个“光”操作员的相关函数的结果。特别是，我们确定了“重型轻” OPE系数的形式，其功能是费用和$ d $的函数。
We study operators in the rank-$j$ totally symmetric representation of $O(N)$ in the critical $O(N)$ model in arbitrary dimension $d$, in the limit of large $N$ and large charge $j$ with $j/N\equiv \hat{j}$ fixed. The scaling dimensions of the operators in this limit may be obtained by a semiclassical saddle point calculation. Using the standard Hubbard-Stratonovich description of the critical $O(N)$ model at large $N$, we solve the relevant saddle point equation and determine the scaling dimensions as a function of $d$ and $\hat{j}$, finding agreement with all existing results in various limits. In $4<d<6$, we observe that the scaling dimension of the large charge operators becomes complex above a critical value of the ratio $j/N$, signaling an instability of the theory in that range of $d$. Finally, we also derive results for the correlation functions involving two "heavy" and one or two "light" operators. In particular, we determine the form of the "heavy-heavy-light" OPE coefficients as a function of the charges and $d$.
