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arXiv · 2006.07374

The Inversion Formula and 6j Symbol for 3d Fermions

Soner Albayrak·David Meltzer·David Poland
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Abstract

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.

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Soner Albayrak, David Meltzer, David Poland. 2020-06-12. The Inversion Formula and 6j Symbol for 3d Fermions. https://doi.org/10.1007/jhep09(2020)148

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