Conformal symmetry and composite operators in the O(N)3 tensor field theory
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 tetrahed...
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| Main Authors: | , , |
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| Format: | Article (Journal) Chapter/Article |
| Language: | English |
| Published: |
25 Mar 2020
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| Edition: | Version v2 |
| In: |
Arxiv
Year: 2020, Pages: 1-44 |
| Online Access: | Verlag, lizenzpflichtig, Volltext: http://arxiv.org/abs/2002.07652
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| Author Notes: | Dario Benedetti, Razvan Gurau and Kenta Suzuki |
| Summary: | 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. |
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| Item Description: | Im Titel ist die Zahl "3" hochgestellt Version 1 vom 18. Februar 2020, Version 2 vom 25. März 2020 Gesehen am 07.10.2022 |
| Physical Description: | Online Resource |