论文标题
3D费米子的反转公式和6J符号
The Inversion Formula and 6j Symbol for 3d Fermions
论文作者
论文摘要
在这项工作中，我们研究了费米金运营商的$ 3D $共形组的$ 6J $象征。特别是，我们研究了包含两个费米子和两个标量的四点函数，还有四个具有四个费米子的功能。通过为Euclidean Condomatal组使用重量转移操作员和谐波分析，我们将这些旋转$ 6J $符号与四个标量算子的简单$ 6J $符号联系起来。作为一种应用程序，我们使用这些技术来计算费米子操作员的$ 3D $平均场理论（MFT）OPE系数。然后，由于单个操作员的反转（例如应力张量或低维标量），我们将校正到MFT频谱和耦合。这些结果在有限自旋时有效，并扩展了扰动大型自旋分析，以在自旋中包括非扰动效应。
In this work we study the $6j$ symbol of the $3d$ conformal group for fermionic operators. In particular, we study 4-point functions containing two fermions and two scalars and also those with four fermions. By using weight-shifting operators and harmonic analysis for the Euclidean conformal group, we relate these spinning $6j$ symbols to the simpler $6j$ symbol for four scalar operators. As one application we use these techniques to compute $3d$ mean field theory (MFT) OPE coefficients for fermionic operators. We then compute corrections to the MFT spectrum and couplings due to the inversion of a single operator, such as the stress tensor or a low-dimension scalar. These results are valid at finite spin and extend the perturbative large spin analysis to include non-perturbative effects in spin.
