3d费米子的反演公式和6j符号
The Inversion Formula and 6j Symbol for 3d Fermions
摘要：
本文研究了费米子算符共形群$3d$的$6j$符号。特别地，我们研究了含有两个费米子和两个标量的四点函数，以及含有四个费米子的四点函数。通过对欧氏共形群使用权移算子和调和分析，我们将这些自旋$6j$符号与四个标量算子的更简单的$6j$符号联系起来。作为一个应用程序，我们使用这些技术来计算$3d$平均场论（MFT）OPE系数的费米子运营商。然后，我们计算修正MFT频谱和耦合由于一个单一的运营商，如应力张量或低维标量的反演。这些结果在有限自旋下是有效的，并将微扰大自旋分析推广到包括自旋中的非微扰效应。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
