Bifurcation of fixed points in a O(N)-symmetric ( 2+1 )-dimensional gauged Φ6 theory with a Chern-Simons term

Abstract

We examine the phase structure of an Abelian Chern-Simons system with relativistic charged matter fields with a sixth-order potential. Using a large $N$ technique, we compute the quantum effective potential and the renormalization group function of the coupling to the next-to-leading order of the $1/N$ expansion in terms of the Chern-Simons coefficient. The model has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone mode. We show that the beta function of the sextic coupling exhibits, at the next order in the $1/N$ expansion, nontrivial running that we analyze explicitly in terms of the Chern-Simons coefficient. Viewed as a dynamical system, the renormalization group (RG) flow exhibits a topological normal form of a generic one-dimensional system having a fold bifurcation. We demonstrate that the corresponding IR and UV fixed points, each describing a conformal phase of the theory, approach each other until they merge, giving rise to a scaling behavior similar to Berezinskii-Kosterlitz-Thouless phase transitions. Our study identifies a window in the parameter space of the Chern-Simons coefficient where the renormalization group flow has a stable infrared fixed point and where scale invariance is recovered. We also find that the Chern-Simons interaction modifies the scaling dimension of the operator crossing marginality at the bifurcation points.