We study correlation functions of a conserved spin-1 current Jμ in three dimensional Conformal Field Theories (CFTs). We investigate the constraints imposed by permutation symmetry and current conservation on the form of three point functions ⟨JμJνOΔ,ℓ⟩ and the four point function ⟨JμJνJρJσ⟩ and identify the minimal set of independent crossing symmetry conditions. We obtain a recurrence relation for conformal blocks for generic spin-1 operators in three dimensions. In the process, we improve several technical points, facilitating the use of recurrence relations. By applying the machinery of the numerical conformal bootstrap we obtain universal bounds on the dimensions of certain light operators as well as the central charge. Highlights of our results include numerical evidence for the conformal collider bound and new constraints on the parameters of the critical O(2) model. The results obtained in this work apply to any unitary, three dimensional CFT.
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Article funded by SCOAP3.
AD is supported by NSF grant PHY-1720374. AV is supported by the Swiss National Science Foundation under grant no. PP00P2-163670. JP is supported by the National Centre of Competence in Research SwissMAP funded by the Swiss National Science Foundation and by the Simons collaboration on the Non-perturbative Bootstrap funded by the Simons Foundation. ET is supported by the Portuguese Fundação para a Ciência e a Tecnologia (FCT) through the fellowship SFRH/BD/51984/2012. ET is also partially supported by Perimeter Institute for Theoretical Physics. ET would like to thank FAPESP grant 2011/11973-4 for funding his visit to ICTP-SAIFR where a part of this work was done.
Dymarsky, Anatoly; Penedones, Joao; Trevisani, Emilio; and Vichi, Alessandro, "Charting the Space of 3D CFTs with a Continuous Global Symmetry" (2019). Physics and Astronomy Faculty Publications. 664.