发表机构
Abdus Salam Centre for Theoretical Physics, Imperial College London; Departement de physique, Universite de Montreal（阿卜杜斯·萨拉姆理论物理中心，伦敦帝国理工学院; 蒙特利尔大学物理系）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文计算了Chern-Simons QED$_3$中磁单极子算符的标度维度，验证了与标量QED$_3$的对偶性，并发现大电荷极限下$q^0$项与宇称保持理论的普适EFT一致。
AI 中文摘要
我们计算了QED$_3$中电荷为$q$的磁单极子算符的标度维度，其中包含$N$个二分量复费米子，Chern-Simons能级为$k$，在$k,N$很大且$k/N$固定的极限下计算至次领头阶。我们利用这一结果以及先前关于标量QED$_3$（sQED$_3$）的结果，检验了$N=1,k=-3/2$的QED$_3$与$N=1,k=2$的sQED$_3$之间的对偶性，后者的$U(1)$磁单极子对称性增强为$SO(3)$。我们发现QED$_3$的最低电荷磁单极子值接近2，这与涌现的$SO(3)$流相符；第二低电荷磁单极子与模糊球计算给出的预言一致，而更高电荷$q$的磁单极子与相应sQED$_3$的值匹配，相对误差仅为百分之一。我们还发现了类似证据，支持$N=1,k=-(2m+1)/2$的QED$_3$与一个标量耦合到两个$U(1)$规范场之间的对偶性，后者在$m>1$时具有$N=1,k=\ rac{m+1}{m}$且$q_s=mq_f$的sQED$_3$有效描述。最后，通过拟合多个$q$值，我们表明QED$_3$在大$q$时的$q^0$项取与宇称保持$U(1)$理论的普适EFT中相同的非零值，尽管在$k\ eq0$时宇称被破坏。对于sQED$_3$，类似的拟合在$k\ eq0$时给出零$q^0$项，这与先前在$k=0$时观察到的普适非零值不同。
英文摘要
We compute the scaling dimensions of charge $q$ monopole operators in QED$_3$ with $N$ two-component complex fermions and Chern-Simons level $k$, to subleading order in the limit where $k,N$ are large and $k/N$ is fixed. We use this and previous results for scalar QED$_3$ (sQED$_3$) to check the duality between QED$_3$ with $N=1,k=-3/2$ and sQED$_3$ with $N=1,k=2$, whose $U(1)$ monopole symmetry is enhanced to $SO(3)$. We find that the lowest charge monopole value for QED$_3$ is close to 2 as expected for the emergent $SO(3)$ current, the second lowest charge monopole matches a prediction from a fuzzy sphere calculation, while higher $q$ monopoles match the corresponding sQED$_3$ values with relative error of just one percent. We also find similar evidence for dualities between QED$_3$ with $N=1,k=-(2m+1)/2$ and one scalar coupled to two $U(1)$ gauge fields, which has an effective description as sQED$_3$ with $N=1,k=\frac{m+1}{m}$ and $q_s=mq_f$ for $m>1$. Finally, by fitting many values of $q$ we show that the $q^0$ term at large $q$ for QED$_3$ takes the same nonzero value that appears in the universal EFT for parity preserving $U(1)$ theories, even though parity is broken for $k\neq0$. For sQED$_3$, a similar fit gives zero $q^0$ term for $k\neq0$, unlike the universal nonzero value previously observed for $k=0$.
Comments26 pages plus appendices
