The inversion formula and 6j symbol for 3d fermions
The inversion formula and 6j symbol for 3d fermions
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3d 费米子的反演公式和 6j 符号
DOI：
10.1007/jhep09(2020)148
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发表时间：
2020
影响因子：
5.4
通讯作者：
David Poland
中科院分区：
文献类型：
--
作者：
Soner Albayrak;David Meltzer;David Poland
本文研究了费米子算符三维共形群的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。通过使用权移算子和调和分析的欧几里得共形群，我们将这些旋转6j符号简单的6j符号的四个标量算子。作为一个应用程序，我们使用这些技术来计算三维平均场理论（MFT）的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。
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.