Conformal symmetry and composite operators in the O(N )3 tensor field theory - Dario Benedetti (Journal of High Energy Physics, 2020)
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 𝜙 4 composite operators, known as tetrahedron, pillow and double-trace. As shown in [1, 2], 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 𝜙 4 and 𝜙 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.