论文标题
轻射线OP中的横向自旋
Transverse spin in the light-ray OPE
论文作者
论文摘要
我们研究了无效的本地操作员的产品$ \ Mathcal {O} _1 $和$ \ Mathcal {O} _2 $在CFT中的同一空平面上。这种无效的综合运算符在虚拟的$ d-2 $尺寸CFT中的指示中横向到无效积分的方向上的原始运算符。我们在这些横向方向上对OPE进行完整描述。低横向旋转的术语是带有旋转$ j_1+j_2-1 $的轻射线操作员。具有较高横向自旋的术语是带有较高旋转$ J_1+J_2-1+N $的光线运算符的主要后代，该术语是使用特殊不变的差速器算子构建的，这些差速器的构建精确地出现在光射线OPE的运动学中。例如，平均无效能源操作员之间的OPE包含带有旋转$ 3 $的轻射射线操作员（如Hofman和Maldacena所述），但同时还包含具有旋转$ 5,7,9，$等的新颖术语。这些新术语对于描述能量能量的两点相关器很重要，以描述非固定对称性状态的两点相关器，以及计算多功能点能量corelators。我们在$ \ Mathcal {n} = 4 $ sym中以非旋转对称的能量相关器检查我们的公式，找到完美的一致性。
We study a product of null-integrated local operators $\mathcal{O}_1$ and $\mathcal{O}_2$ on the same null plane in a CFT. Such null-integrated operators transform like primaries in a fictitious $d-2$ dimensional CFT in the directions transverse to the null integrals. We give a complete description of the OPE in these transverse directions. The terms with low transverse spin are light-ray operators with spin $J_1+J_2-1$. The terms with higher transverse spin are primary descendants of light-ray operators with higher spins $J_1+J_2-1+n$, constructed using special conformally-invariant differential operators that appear precisely in the kinematics of the light-ray OPE. As an example, the OPE between average null energy operators contains light-ray operators with spin $3$ (as described by Hofman and Maldacena), but also novel terms with spin $5,7,9,$ etc.. These new terms are important for describing energy two-point correlators in non-rotationally-symmetric states, and for computing multi-point energy correlators. We check our formulas in a non-rotationally-symmetric energy correlator in $\mathcal{N}=4$ SYM, finding perfect agreement.
