Recursion relation for general 3d blocks
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)