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 ^[1]

Ecole Polytechnique Federale Lausanne (Switzlerland). Inst. of Physics
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)

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:: Institute for Advanced Study, Princeton, NJ (United States)

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

Grant/Contract Number:: SC0009988; PP00P2-163670

OSTI ID:: 1596663

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

Publisher:: Springer BerlinCopyright Statement

Country of Publication:: United States

Language:: English

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Cited by: 32 works

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