Conformal Symmetry and Composite Operators in the $O(N)^3$ Tensor Field Theory

Understand

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.