The inversion formula and 6j symbol for 3d fermions

@article{Albayrak2020TheIF,
  title={The inversion formula and 6j symbol for 3d fermions},
  author={Soner Albayrak and David Meltzer and David Poland},
  journal={arXiv: High Energy Physics - Theory},
  year={2020}
}
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… Expand

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References

SHOWING 1-10 OF 47 REFERENCES
Scalar-fermion analytic bootstrap in 4D
A bstractIn this work we discuss an analytic bootstrap approach [1, 2] in the context of spinning 4D conformal blocks [3, 4]. As an example we study the simplest spinning case, the scalar-fermionExpand
More analytic bootstrap: nonperturbative effects and fermions
Abstract We develop the analytic bootstrap in several directions. First, we discuss the appearance of nonperturbative effects in the Lorentzian inversion formula, which are exponentiallyExpand
d-dimensional SYK, AdS loops, and 6j symbols
A bstractWe study the 6j symbol for the conformal group, and its appearance in three seemingly unrelated contexts: the SYK model, conformal representation theory, and perturbative amplitudes in AdS.Expand
Bootstrapping 3D fermions
A bstractWe study the conformal bootstrap for a 4-point function of fermions 〈ψψψψ〉 in 3D. We first introduce an embedding formalism for 3D spinors and compute the conformal blocks appearing inExpand
Conformal collider physics from the lightcone bootstrap
A bstractWe analytically study the lightcone limit of the conformal bootstrap equations for 4-point functions containing global symmetry currents and the stress tensor in 3d CFTs. We show that theExpand
The lightcone bootstrap and the spectrum of the 3d Ising CFT
We compute numerically the dimensions and OPE coefficients of several operators in the 3d Ising CFT, and then try to reverse-engineer the solution to crossing symmetry analytically. Our key tool is aExpand
Resummation at finite conformal spin
A bstractWe generalize the computation of anomalous dimension and correction to OPE coefficients at finite conformal spin considered recently in [1, 2] to arbitrary space-time dimensions. By usingExpand
Conformal bootstrap in the Regge limit
A bstractWe analytically solve the conformal bootstrap equations in the Regge limit for large N conformal field theories. For theories with a parametrically large gap, the amplitude is dominated byExpand
Anomalous dimensions at finite conformal spin from OPE inversion
A bstractWe compute anomalous dimensions of higher spin operators in Conformal Field Theory at arbitrary space-time dimension by using the OPE inversion formula of [1], both from the position spaceExpand
Weight shifting operators and conformal blocks
A bstractWe introduce a large class of conformally-covariant differential operators and a crossing equation that they obey. Together, these tools dramatically simplify calculations involvingExpand
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4
5
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