Fermion conformal bootstrap in 4d

Karateev, Denis; Kravchuk, Petr; Serone, Marco; Vichi, Alessandro

doi:10.1007/JHEP06(2019)088

Title: Fermion conformal bootstrap in 4d

Journal Article · 18 June 2019 · Journal of High Energy Physics (Online)

DOI: https://doi.org/10.1007/JHEP06(2019)088 · OSTI ID:1596663

^[1]; Kravchuk, Petr ^[2]; Serone, Marco ^[3]; Vichi, Alessandro ^[4]

Ecole Polytechnique Federale Lausanne (Switzlerland). Inst. of Physics; Institute for Advanced Study
Inst. for Advanced Study, Princeton, NJ (United States). School of Natural Sciences
National Inst. of Nuclear Physics (INFN), Trieste (Italy); International School for Advanced Studies (SISSA), Trieste (Italy)
Ecole Polytechnique Federale Lausanne (Switzlerland). Inst. of Physics

We apply numerical conformal bootstrap techniques to the four-point function of a Weyl spinor in 4d non-supersymmetric CFTs. We find universal bounds on operator dimensions and OPE coefficients, including bounds on operators in mixed symmetry representations of the Lorentz group, which were inaccessible in previous bootstrap studies. We find discontinuities in some of the bounds on operator dimensions, and we show that they arise due to a generic yet previously unobserved “fake primary” effect, which is related to the existence of poles in conformal blocks. We show that this effect is also responsible for similar discontinuities found in four-fermion bootstrap in 3d, as well as in the mixed-correlator analysis of the 3d Ising CFT. As an important byproduct of our work, we develop a practical technology for numerical approximation of general 4d conformal blocks.

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

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

Grant/Contract Number:: SC0009988

OSTI ID:: 1596663

Journal Information:: Journal of High Energy Physics (Online), Journal Name: Journal of High Energy Physics (Online) Journal Issue: 6 Vol. 2019; ISSN 1029-8479

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

References (79)

Implications of Conformal Invariance in Field Theories for General Dimensions Osborn, H.; Petkou, A. Annals of Physics, Vol. 231, Issue 2 https://doi.org/10.1006/aphy.1994.1045	journal	May 1994
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
Improved bounds for CFT’s with global symmetries Vichi, Alessandro Journal of High Energy Physics, Vol. 2012, Issue 1 https://doi.org/10.1007/JHEP01(2012)162	journal	January 2012
General three-point functions in 4D CFT Elkhidir, Emtinan; Karateev, Denis; Serone, Marco Journal of High Energy Physics, Vol. 2015, Issue 1 https://doi.org/10.1007/JHEP01(2015)133	journal	January 2015
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
Seed conformal blocks in 4D CFT Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis Journal of High Energy Physics, Vol. 2016, Issue 2 https://doi.org/10.1007/JHEP02(2016)183	journal	February 2016
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
The analytic functional bootstrap. Part I: 1D CFTs and 2D S-matrices Mazáč, Dalimil; Paulos, Miguel F. Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)162	journal	February 2019
The analytic functional bootstrap. Part II. Natural bases for the crossing equation Mazáč, Dalimil; Paulos, Miguel F. Journal of High Energy Physics, Vol. 2019, Issue 2 https://doi.org/10.1007/JHEP02(2019)163	journal	February 2019
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
The lightcone bootstrap and the spectrum of the 3d Ising CFT Simmons-Duffin, David Journal of High Energy Physics, Vol. 2017, Issue 3 https://doi.org/10.1007/JHEP03(2017)086	journal	March 2017
Extremal bootstrapping: go with the flow El-Showk, Sheer; Paulos, Miguel F. Journal of High Energy Physics, Vol. 2018, Issue 3 https://doi.org/10.1007/JHEP03(2018)148	journal	March 2018
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
Analytic bounds and emergence of AdS2 physics from the conformal bootstrap Mazáč, Dalimil Journal of High Energy Physics, Vol. 2017, Issue 4 https://doi.org/10.1007/JHEP04(2017)146	journal	April 2017
Bounds on 4D conformal and superconformal field theories Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2011, Issue 5 https://doi.org/10.1007/JHEP05(2011)017	journal	May 2011
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
Notes on spinning operators in fermionic CFT Giombi, S.; Kirilin, V.; Skvortsov, E. Journal of High Energy Physics, Vol. 2017, Issue 5 https://doi.org/10.1007/JHEP05(2017)041	journal	May 2017
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
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
Bootstrap bound for conformal multi-flavor QCD on lattice Nakayama, Yu Journal of High Energy Physics, Vol. 2016, Issue 7 https://doi.org/10.1007/JHEP07(2016)038	journal	July 2016
Bootstrapping mixed correlators in 4D N $$ \mathcal{N} $$ = 1 SCFTs Li, Daliang; Meltzer, David; Stergiou, Andreas Journal of High Energy Physics, Vol. 2017, Issue 7 https://doi.org/10.1007/JHEP07(2017)029	journal	July 2017
A spacetime derivation of the Lorentzian OPE inversion formula Simmons-Duffin, David; Stanford, Douglas; Witten, Edward Journal of High Energy Physics, Vol. 2018, Issue 7 https://doi.org/10.1007/JHEP07(2018)085	journal	July 2018
Covariant approaches to superconformal blocks Fitzpatrick, A. Liam; Kaplan, Jared; Khandker, Zuhair U. Journal of High Energy Physics, Vol. 2014, Issue 8 https://doi.org/10.1007/JHEP08(2014)129	journal	August 2014
Deconstructing conformal blocks in 4D CFT Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis Journal of High Energy Physics, Vol. 2015, Issue 8 https://doi.org/10.1007/JHEP08(2015)101	journal	August 2015
Precision islands in the Ising and O(N ) models Kos, Filip; Poland, David; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2016, Issue 8 https://doi.org/10.1007/JHEP08(2016)036	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
Analyticity in spin in conformal theories Caron-Huot, Simon Journal of High Energy Physics, Vol. 2017, Issue 9 https://doi.org/10.1007/JHEP09(2017)078	journal	September 2017
Bounds on OPE coefficients in 4D Conformal Field Theories Caracciolo, Francesco; Echeverri, Alejandro Castedo; von Harling, Benedict Journal of High Energy Physics, Vol. 2014, Issue 10 https://doi.org/10.1007/JHEP10(2014)020	journal	October 2014
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
Convexity and liberation at large spin Komargodski, Zohar; Zhiboedov, Alexander Journal of High Energy Physics, Vol. 2013, Issue 11 https://doi.org/10.1007/JHEP11(2013)140	journal	November 2013
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
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David Journal of High Energy Physics, Vol. 2018, Issue 11 https://doi.org/10.1007/JHEP11(2018)102	journal	November 2018
The analytic bootstrap and AdS superhorizon locality Fitzpatrick, A. Liam; Kaplan, Jared; Poland, David Journal of High Energy Physics, Vol. 2013, Issue 12 https://doi.org/10.1007/JHEP12(2013)004	journal	December 2013
Solving the 3d Ising Model with the Conformal Bootstrap II. $$c$$ c -Minimization and Precise Critical Exponents El-Showk, Sheer; Paulos, Miguel F.; Poland, David Journal of Statistical Physics, Vol. 157, Issue 4-5 https://doi.org/10.1007/s10955-014-1042-7	journal	June 2014
Finite-component field representations of the conformal group Mack, G.; Salam, Abdus Annals of Physics, Vol. 53, Issue 1 https://doi.org/10.1016/0003-4916(69)90278-4	journal	June 1969
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
On the phase structure of vector-like gauge theories with massless fermions Banks, T.; Zaks, A. Nuclear Physics B, Vol. 196, Issue 2 https://doi.org/10.1016/0550-3213(82)90035-9	journal	March 1982
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
Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach Iha, Hisashi; Makino, Hiroki; Suzuki, Hiroshi Progress of Theoretical and Experimental Physics, Vol. 2016, Issue 5 https://doi.org/10.1093/ptep/ptw046	journal	May 2016
Bootstrapping Conformal Field Theories with the Extremal Functional Method El-Showk, Sheer; Paulos, Miguel F. Physical Review Letters, Vol. 111, Issue 24 https://doi.org/10.1103/PhysRevLett.111.241601	journal	December 2013
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
Asymptotic Behavior of Non-Abelian Gauge Theories to Two-Loop Order Caswell, William E. Physical Review Letters, Vol. 33, Issue 4 https://doi.org/10.1103/PhysRevLett.33.244	journal	July 1974
Lattice tests of beyond standard model dynamics DeGrand, Thomas Reviews of Modern Physics, Vol. 88, Issue 1 https://doi.org/10.1103/RevModPhys.88.015001	journal	January 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
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
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
Bounds on 4D Conformal and Superconformal Field Theories Poland, David; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1009.2087	text	January 2010
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 Conformal Field Theories with the Extremal Functional Method El-Showk, Sheer; Paulos, Miguel F. arXiv https://doi.org/10.48550/arxiv.1211.2810	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
Covariant Approaches to Superconformal Blocks Fitzpatrick, A. Liam; Kaplan, Jared; Khandker, Zuhair U. arXiv https://doi.org/10.48550/arxiv.1402.1167	text	January 2014
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
Bounds on OPE Coefficients in 4D Conformal Field Theories Caracciolo, Francesco; Echeverri, Alejandro Castedo; von Harling, Benedict arXiv https://doi.org/10.48550/arxiv.1406.7845	text	January 2014
Deconstructing Conformal Blocks in 4D CFT Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis arXiv https://doi.org/10.48550/arxiv.1505.03750	preprint	January 2015
Bootstrapping 3D Fermions Iliesiu, Luca; Kos, Filip; Poland, David arXiv https://doi.org/10.48550/arxiv.1508.00012	text	January 2015
Seed Conformal Blocks in 4D CFT Echeverri, Alejandro Castedo; Elkhidir, Emtinan; Karateev, Denis arXiv https://doi.org/10.48550/arxiv.1601.05325	text	January 2016
Upper bound on the mass anomalous dimension in many-flavor gauge theories: a conformal bootstrap approach Iha, Hisashi; Makino, Hiroki; Suzuki, Hiroshi arXiv https://doi.org/10.48550/arxiv.1603.01995	text	January 2016
Precision Islands in the Ising and $O(N)$ Models Kos, Filip; Poland, David; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1603.04436	text	January 2016
Counting Conformal Correlators Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1612.08987	preprint	January 2016
Notes on Spinning Operators in Fermionic CFT Giombi, S.; Kirilin, V.; Skvortsov, E. arXiv https://doi.org/10.48550/arxiv.1701.06997	text	January 2017
Bootstrapping Mixed Correlators in 4D $\mathcal{N}=1$ SCFTs Li, Daliang; Meltzer, David; Stergiou, Andreas arXiv https://doi.org/10.48550/arxiv.1702.00404	text	January 2017
Analyticity in Spin in Conformal Theories Caron-Huot, Simon arXiv https://doi.org/10.48550/arxiv.1703.00278	text	January 2017
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
Light-ray operators in conformal field theory Kravchuk, Petr; Simmons-Duffin, David arXiv https://doi.org/10.48550/arxiv.1805.00098	text	January 2018
The Conformal Bootstrap: Theory, Numerical Techniques, and Applications Poland, David; Rychkov, Slava; Vichi, Alessandro arXiv https://doi.org/10.48550/arxiv.1805.04405	text	January 2018

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Recursion relation for general 3d blocks Erramilli, Rajeev S.; Iliesiu, Luca V.; Kravchuk, Petr Journal of High Energy Physics, Vol. 2019, Issue 12 https://doi.org/10.1007/jhep12(2019)116	journal	December 2019

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