Conformal symmetry and composite operators in the O(N)3 tensor field theory

• Verfasst von: Benedetti, Dario [VerfasserIn]
• Verfasst von: Gurǎu, Rǎzvan [VerfasserIn]
• Verfasst von: Suzuki, Kenta [VerfasserIn]
• Titel: Conformal symmetry and composite operators in the O(N)3 tensor field theory
• Verf.angabe: Dario Benedetti, Razvan Gurau and Kenta Suzuki
• Ausgabe: Version v2
• E-Jahr: 2020
• Jahr: 25 Mar 2020
• Umfang: 44 S.
• Fussnoten: Im Titel ist die Zahl "3" hochgestellt ; Version 1 vom 18. Februar 2020, Version 2 vom 25. März 2020 ; Gesehen am 07.10.2022
• Titel Quelle: Enthalten in: De.arxiv.org
• Ort Quelle: [S.l.] : Arxiv.org, 1991
• Jahr Quelle: 2020
• Band/Heft Quelle: (2020), Artikel-ID 2002.07652, Seite 1-44
• DOI: doi:10.48550/arXiv.2002.07652
• Datenträger: Online-Ressource
• Sprache: eng
• Sach-SW: High Energy Physics - Theory
• K10plus-PPN: 1804437123

Abstract

We continue the study of the bosonic $O(N)^3$ model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant $\phi^4$ composite operators, known as tetrahedron, pillow and double-trace. As shown in arXiv:1903.03578 and arXiv:1909.07767, the tetrahedron operator is exactly marginal in the large-$N$ limit and for a purely imaginary tetrahedron coupling a line of real infrared fixed points (parametrized by the absolute value of the tetrahedron coupling) is found for the other two couplings. These fixed points have real critical exponents and a real spectrum of bilinear operators, satisfying unitarity constraints. This raises the question whether at large-$N$ the model is unitary, despite the tetrahedron coupling being imaginary. In this paper, we first rederive the above results by a different regularization and renormalization scheme. We then discuss the operator mixing for composite operators and we give a perturbative proof of conformal invariance of the model at the infrared fixed points by adapting a similar proof from the long-range Ising model. At last, we identify the scaling operators at the fixed point and compute the two- and three-point functions of $\phi^4$ and $\phi^2$ composite operators. The correlations have the expected conformal behavior and the OPE coefficients are all real, reinforcing the claim that the large-$N$ CFT is unitary.