Chaotic RG flow in tensor models

Abstract

We study biantisymmetric tensor quantum field theories with O(N-1) x O(N-2) symmetry. Working in 4 - epsilon dimensions we calculate the beta functions up to second order in the coupling constants and analyze in detail the renormalization group (RG) flow and its fixed points. We allow N-1 and N-2 to assume general real values and treat them as bifurcation parameters. In studying the behavior of these models in a nonunitary regime in the space of N-1 and N-2 we find a point where a zero-Hopf bifurcation occurs. In the vicinity of this point, we provide analytical and numerical evidence for the existence of Shilnikov homoclinic orbits, which induce chaotic behavior in the RG flow of a subset of nearby theories. As a simple warm-up example for the study of chaotic RG flows, we also review the non-Hermitian Ising chain and show how, for special complex values of the coupling constant, its RG transformations are equivalent to the Bernoulli map.