English

Recursion relation for general 3d blocks

High Energy Physics - Theory 2020-01-29 v2 Mathematical Physics math.MP

Abstract

We derive closed-form expressions for all ingredients of the Zamolodchikov-like recursion relation for general spinning conformal blocks in 3-dimensional conformal field theory. This result opens a path to efficient automatic generation of conformal block tables, which has immediate applications in numerical conformal bootstrap program. Our derivation is based on an understanding of null states and conformally-invariant differential operators in momentum space, combined with a careful choice of the relevant tensor structures bases. This derivation generalizes straightforwardly to higher spacetime dimensions d, provided the relevant Clebsch-Gordan coefficients of Spin(d) are known.

Keywords

Cite

@article{arxiv.1907.11247,
  title  = {Recursion relation for general 3d blocks},
  author = {Rajeev S. Erramilli and Luca V. Iliesiu and Petr Kravchuk},
  journal= {arXiv preprint arXiv:1907.11247},
  year   = {2020}
}

Comments

43 pages plus appendices, 2 figures (v2: fixed typos; added 2 references, fixed 3 references; updated acknowledgements)

R2 v1 2026-06-23T10:31:14.511Z