Conformal symmetry and composite operators in the \(O(N )^3\) tensor field theory
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Publication:783928
DOI10.1007/JHEP06(2020)113zbMATH Open1437.81069arXiv2002.07652MaRDI QIDQ783928
Author name not available (Why is that?)
Publication date: 4 August 2020
Published in: (Search for Journal in Brave)
Abstract: We continue the study of the bosonic model with quartic interactions and long-range propagator. The symmetry group allows for three distinct invariant 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- 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- 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 and composite operators. The correlations have the expected conformal behavior and the OPE coefficients are all real, reinforcing the claim that the large- CFT is unitary.
Full work available at URL: https://arxiv.org/abs/2002.07652
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