Recursion relation for general 3d blocks

Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr

doi:10.1007/JHEP12(2019)116

Title: Recursion relation for general 3d blocks

Journal Article · 15 December 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP12(2019)116 · OSTI ID:1596664

Erramilli, Rajeev S. ^[1]; Iliesiu, Luca V. ^[2];

^[3]

Yale Univ., New Haven, CT (United States). Dept. of Physics; Institute for Advanced Study
Princeton Univ., NJ (United States). Joseph Henry Lab. of Physics
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences

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.

View Accepted Manuscript (DOE)

Cite

Export

Save

Research Organization:: Inst. for Advanced Study, Princeton, NJ (United States)

Sponsoring Organization:: USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25); Simons Foundation

Contributing Organization:: Perimeter Institute for Theoretical Physics

Grant/Contract Number:: SC0009988

OSTI ID:: 1596664

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 12 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (60)

Conformal symmetry in two-dimensional space: Recursion representation of conformal block Zamolodchikov, Al. B. Theoretical and Mathematical Physics, Vol. 73, Issue 1 https://doi.org/10.1007/BF01022967	journal	October 1987
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, G. Communications in Mathematical Physics, Vol. 55, Issue 1 https://doi.org/10.1007/BF01613145	journal	February 1977
Bootstrapping 3D fermions with global symmetries Iliesiu, Luca; Kos, Filip; Poland, David Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)036	journal	January 2018
General bootstrap equations in 4D CFTs Cuomo, Gabriel Francisco; Karateev, Denis; Kravchuk, Petr Journal of High Energy Physics, Vol. 2018, Issue 1 https://doi.org/10.1007/JHEP01(2018)130	journal	January 2018
Casimir recursion relations for general conformal blocks Kravchuk, Petr Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)011	journal	February 2018
Weight shifting operators and conformal blocks Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)081	journal	February 2018
Counting conformal correlators Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)096	journal	February 2018
The 3d stress-tensor bootstrap Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr Journal of High Energy Physics, Vol. 2018, Issue 2 https://doi.org/10.1007/JHEP02(2018)164	journal	February 2018
Bootstrapping 3D fermions Iliesiu, Luca; Kos, Filip; Poland, David Journal of High Energy Physics, Vol. 2016, Issue 3 https://doi.org/10.1007/JHEP03(2016)120	journal	March 2016
Projectors, shadows, and conformal blocks Simmons-Duffin, David Journal of High Energy Physics, Vol. 2014, Issue 4 https://doi.org/10.1007/JHEP04(2014)146	journal	April 2014
Scale anomalies, states, and rates in conformal field theory Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A. Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)171	journal	April 2017
Carving out the space of 4D CFTs Poland, David; Simmons-Duffin, David; Vichi, Alessandro Journal of High Energy Physics, Vol. 2012, Issue 5 https://doi.org/10.1007/JHEP05(2012)110	journal	May 2012
Monopole operators in U(1) Chern-Simons-matter theories Chester, Shai M.; Iliesiu, Luca V.; Mezei, Márk Journal of High Energy Physics, Vol. 2018, Issue 5 https://doi.org/10.1007/JHEP05(2018)157	journal	May 2018
Bootstrapping the O(N ) vector models Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2014, Issue 6 https://doi.org/10.1007/JHEP06(2014)091	journal	June 2014
A semidefinite program solver for the conformal bootstrap Simmons-Duffin, David Journal of High Energy Physics, Vol. 2015, Issue 6 https://doi.org/10.1007/JHEP06(2015)174	journal	June 2015
autoboot: a generator of bootstrap equations with global symmetry Go, Mocho; Tachikawa, Yuji Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/JHEP06(2019)084	journal	June 2019
Fermion conformal bootstrap in 4d Karateev, Denis; Kravchuk, Petr; Serone, Marco Journal of High Energy Physics, Vol. 2019, Issue 6 https://doi.org/10.1007/JHEP06(2019)088	journal	June 2019
Projectors and seed conformal blocks for traceless mixed-symmetry tensors Costa, Miguel S.; Hansen, Tobias; Penedones, João Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)018	journal	July 2016
Radial expansion for spinning conformal blocks Costa, Miguel S.; Hansen, Tobias; Penedones, João Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)057	journal	July 2016
Diagonal limit for conformal blocks in d dimensions Hogervorst, Matthijs; Osborn, Hugh; Rychkov, Slava Journal of High Energy Physics, Vol. 2013, Issue 8 https://doi.org/10.1007/JHEP08(2013)014	journal	August 2013
N $$ \mathcal{N} $$ = 1 superconformal blocks for general scalar operators Khandker, Zuhair U.; Li, Daliang; Poland, David Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)049	journal	August 2014
Towards bootstrapping QED3 Chester, Shai M.; Pufu, Silviu S. Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)019	journal	August 2016
Recursion relations for conformal blocks Penedones, João; Trevisani, Emilio; Yamazaki, Masahito Journal of High Energy Physics, Vol. 2016, Issue 9 https://doi.org/10.1007/JHEP09(2016)070	journal	September 2016
Graviton scattering and a sum rule for the c anomaly in 4D CFT Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A. Journal of High Energy Physics, Vol. 2018, Issue 9 https://doi.org/10.1007/JHEP09(2018)025	journal	September 2018
The conformal bootstrap at finite temperature Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)070	journal	October 2018
Momentum-space conformal blocks on the light cone Gillioz, Marc Journal of High Energy Physics, Vol. 2018, Issue 10 https://doi.org/10.1007/JHEP10(2018)125	journal	October 2018
Harmonic analysis and mean field theory Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2019, Issue 10 https://doi.org/10.1007/JHEP10(2019)217	journal	October 2019
Spinning conformal correlators Costa, Miguel S.; Penedones, João; Poland, David Journal of High Energy Physics, Vol. 2011, Issue 11 https://doi.org/10.1007/JHEP11(2011)071	journal	November 2011
Spinning conformal blocks Costa, Miguel S.; Penedones, João; Poland, David Journal of High Energy Physics, Vol. 2011, Issue 11 https://doi.org/10.1007/JHEP11(2011)154	journal	November 2011
Bootstrapping mixed correlators in the 3D Ising model Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2014, Issue 11 https://doi.org/10.1007/JHEP11(2014)109	journal	November 2014
Tensor representations of conformal algebra and conformally covariant operator product expansion Ferrara, S.; Grillo, A. F.; Gatto, R. Annals of Physics, Vol. 76, Issue 1 https://doi.org/10.1016/0003-4916(73)90446-6	journal	March 1973
Duality in quantum field theory Mack, G. Nuclear Physics B, Vol. 118, Issue 5 https://doi.org/10.1016/0550-3213(77)90238-3	journal	February 1977
Conformal four point functions and the operator product expansion Dolan, F. A.; Osborn, H. Nuclear Physics B, Vol. 599, Issue 1-2 https://doi.org/10.1016/S0550-3213(01)00013-X	journal	April 2001
Conformal partial waves and the operator product expansion Dolan, F. A.; Osborn, H. Nuclear Physics B, Vol. 678, Issue 1-2 https://doi.org/10.1016/j.nuclphysb.2003.11.016	journal	February 2004
Bounding scalar operator dimensions in 4 D CFT Rattazzi, Riccardo; Rychkov, Vyacheslav S.; Tonni, Erik Journal of High Energy Physics, Vol. 2008, Issue 12 https://doi.org/10.1088/1126-6708/2008/12/031	journal	December 2008
Necessary Condition for Emergent Symmetry from the Conformal Bootstrap Nakayama, Yu; Ohtsuki, Tomoki Physical Review Letters, Vol. 117, Issue 13 https://doi.org/10.1103/PhysRevLett.117.131601	journal	September 2016
The conformal bootstrap: Theory, numerical techniques, and applications Poland, David; Rychkov, Slava; Vichi, Alessandro Reviews of Modern Physics, Vol. 91, Issue 1 https://doi.org/10.1103/RevModPhys.91.015002	journal	January 2019
Quantum Theory of Angular Momentum Varshalovich, D. A.; Moskalev, A. N.; Khersonskii, V. K. https://doi.org/10.1142/0270	book	October 1988
Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion INFN Open Access Repository https://doi.org/10.15161/oar.it/1448286657.72	text	January 1973
Tensor Representations of Conformal Algebra and Conformally Covariant Operator Product Expansion Ferrara, S.; Gatto, R.; Grillo, A. F. INFN Open Access Repository https://doi.org/10.15161/oar.it/1448902386.71	text	January 1971
Duality in Quantum Field Theory Mack, Gerhard Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11734	text	January 1975
All unitary ray representations of the conformal group SU(2,2) with positive energy Mack, Gerhard Deutsches Elektronen-Synchrotron, DESY, Hamburg https://doi.org/10.3204/pubdb-2017-11746	text	January 1975
PyCFTBoot: A Flexible Interface for the Conformal Bootstrap Behan, Connor Communications in Computational Physics, Vol. 22, Issue 1 https://doi.org/10.4208/cicp.OA-2016-0107	journal	May 2017
Restrictions imposed by superconformal invariance on quantum field theories Minwalla, Shiraz Advances in Theoretical and Mathematical Physics, Vol. 2, Issue 4 https://doi.org/10.4310/ATMP.1998.v2.n4.a4	journal	January 1998
Spinning Conformal Blocks Costa, Miguel S.; Penedones, Joao; Poland, David arXiv https://doi.org/10.48550/arxiv.1109.6321	text	January 2011
Projectors, Shadows, and Conformal Blocks Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1204.3894	text	January 2012
Bootstrapping the O(N) Vector Models Kos, Filip; Poland, David; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1307.6856	text	January 2013
Bootstrapping Mixed Correlators in the 3D Ising Model Kos, Filip; Poland, David; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1406.4858	text	January 2014
Bootstrapping 3D Fermions Iliesiu, Luca; Kos, Filip; Poland, David arXiv https://doi.org/10.48550/arxiv.1508.00012	text	January 2015
Towards Bootstrapping QED$_3$ Chester, Shai M.; Pufu, Silviu S. arXiv https://doi.org/10.48550/arxiv.1601.03476	text	January 2016
Radial expansion for spinning conformal blocks Costa, Miguel S.; Hansen, Tobias; Penedones, João arXiv https://doi.org/10.48550/arxiv.1603.05552	text	January 2016
Scale Anomalies, States, and Rates in Conformal Field Theory Gillioz, Marc; Lu, Xiaochuan; Luty, Markus A. arXiv https://doi.org/10.48550/arxiv.1612.07800	text	January 2016
Counting Conformal Correlators Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1612.08987	preprint	January 2016
Bootstrapping 3D Fermions with Global Symmetries Iliesiu, Luca; Kos, Filip; Poland, David arXiv https://doi.org/10.48550/arxiv.1705.03484	text	January 2017
Weight Shifting Operators and Conformal Blocks Karateev, Denis; Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1706.07813	text	January 2017
The 3d Stress-Tensor Bootstrap Dymarsky, Anatoly; Kos, Filip; Kravchuk, Petr arXiv https://doi.org/10.48550/arxiv.1708.05718	text	January 2017
Casimir recursion relations for general conformal blocks Kravchuk, Petr arXiv https://doi.org/10.48550/arxiv.1709.05347	text	January 2017
The Conformal Bootstrap at Finite Temperature Iliesiu, Luca; Koloğlu, Murat; Mahajan, Raghu arXiv https://doi.org/10.48550/arxiv.1802.10266	text	January 2018
Momentum-space conformal blocks on the light cone Gillioz, Marc arXiv https://doi.org/10.48550/arxiv.1807.07003	text	January 2018
Restrictions Imposed by Superconformal Invariance on Quantum Field Theories Minwalla, Shiraz arXiv https://doi.org/10.48550/arxiv.hep-th/9712074	text	January 1997

Similar Records

Casimir recursion relations for general conformal blocks

Journal Article · 2018 · Journal of High Energy Physics (Online) · OSTI ID:1499658

Kravchuk, Petr

blocks_3d: software for general 3d conformal blocks

Journal Article · 2021 · Journal of High Energy Physics (Online) · OSTI ID:1879862

Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr; +3 more

Recursion relations for 5-point conformal blocks

Journal Article · 2021 · Journal of High Energy Physics (Online) · OSTI ID:1976565

Poland, David; Prilepina, Valentina

Related Subjects

72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
Conformal Field Theory
Conformal and W Symmetry

Title: Recursion relation for general 3d blocks

Citation Formats

References (60)

Similar Records

Related Subjects