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Harmonic Analysis and Mean Field Theory

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arxiv 1809.05111 v1 pith:D65G754V submitted 2018-09-13 hep-th

Denis Karateev , Petr Kravchuk , David Simmons-Duffin This is my paper
classification hep-th
keywords operatorsanalysisfieldformulaharmonicincludingmeantheory
verification ladder T0 review T1 audit T2 compute T3 formal
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We review some aspects of harmonic analysis for the Euclidean conformal group, including conformally-invariant pairings, the Plancherel measure, and the shadow transform. We introduce two efficient methods for computing these quantities: one based on weight-shifting operators, and another based on Fourier space. As an application, we give a general formula for OPE coefficients in Mean Field Theory (MFT) for arbitrary spinning operators. We apply this formula to several examples, including MFT for fermions and "seed" operators in 4d, and MFT for currents and stress-tensors in 3d.

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Cited by 4 Pith papers

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Missing Descendants in the Carrollian Conformal Family

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    Including the missing K0 descendant chain completes Carrollian conformal representations and produces C2>0 sectors and two-point correlators fixed only up to functions of Carrollian invariants.

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  3. Cosmological correlators in gravitationally-constrained de Sitter states

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    Cosmological correlators in gravitationally constrained de Sitter states are conformally invariant and differ from QFT vacuum correlators, but relational observables with a heavy background state can reproduce QFT results.

  4. Regge trajectories, detectors, and distributions in the critical ${\rm O}(N)$ model

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    In the critical O(N) model, renormalizing detector and distribution light-ray operators at leading order in 1/N yields Regge intercepts, the leading-twist splitting function, and a BFKL-type anomalous spin.

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