论文标题
关于4D CFT中大型电荷扩展的注释
A note on the large charge expansion in 4d CFT
论文作者
论文摘要
在这封信中，我们讨论了与$ u（1）$对称性相结合场理论中大型电荷扩展的某些普遍预测，主要集中在四维理论上。我们表明，虽然在三个维度上，量子波动是造成与理论无关的$ q^0 $项在缩放尺寸中的$ q^0 $项的存在。以前讨论四维理论的著作未能识别该术语。我们还计算了第一个转基线校正，以对应于对应于最小能量状态的最小能量$ q $和$ q $和$ q+q $的任意主要运算符的OPE系数，包括三个维度和四个维度。此贡献不取决于操作员的插入，与$Δ_Q$中的量子效应类似，在四个维度上，它用$ q $对数缩放。
In this letter, we discuss certain universal predictions of the large charge expansion in conformal field theories with $U(1)$ symmetry, mainly focusing on four-dimensional theories. We show that, while in three dimensions quantum fluctuations are responsible for the existence of a theory-independent $Q^0$ term in the scaling dimension $Δ_Q$ of the lightest operator with fixed charge $Q\gg 1$, in four dimensions the same mechanism provides a universal $Q^0\log Q$ correction to $Δ_Q$. Previous works discussing four-dimensional theories failed in identifying this term. We also compute the first subleading correction to the OPE coefficient corresponding to the insertion of an arbitrary primary operator with small charge $q\ll Q$ in between the minimal energy states with charge $Q$ and $Q+q$, both in three and four dimensions. This contribution does not depend on the operator insertion and, similarly to the quantum effects in $Δ_Q$, in four dimensions it scales logarithmically with $Q$.
