Abstract
We study an N=1 supersymmetric quantum field theory with O(M)×O(N) symmetry. Working in 3-ε dimensions, we calculate the beta functions up to second loop order and analyze in detail the renormalization group (RG) flow and its fixed points. We allow N and M to assume general real values, which results in them functioning as bifurcation parameters. In studying the behavior of the model in the space of M and N, we demarcate the region where the RG flow is nonmonotonic and determine curves along which Hopf bifurcations take place. At a number of points in the space of M and N we find that the model exhibits an interesting phenomenon: at these points the RG flow possesses a fixed point located at real values of the coupling constants g_{i} but with a stability matrix (∂β_{i}/∂g_{j}) that is not diagonalizable and has a Jordan block of size two with zero eigenvalue. Such points correspond to logarithmic conformal field theories and represent Bogdanov-Takens bifurcations, a type of bifurcation known to give rise to a nearby homoclinic orbit-an RG flow that originates and terminates at the same fixed point. In the present example, we are able to employ analytic and numeric evidence to display the existence of the homoclinic RG flow.
Highlights
Introduction.—Since the classic review by Kogut and Wilson [1] on the ε expansion and renormalization group (RG) flow, the general properties of RG flows have been the subject of active research
This loophole was used in deformed Wess-Zumino-Witten models [14,15,16], the coupling constants pass between infinity and minus infinity in order to realize cyclic RG flow
One important step toward uncovering chaotic RG flow is to establish the existence of homoclinic RG flow. In this short Letter, we study a quantum field theories (QFTs) with global OðNÞ × OðMÞ symmetry
Summary
Introduction.—Since the classic review by Kogut and Wilson [1] on the ε expansion and renormalization group (RG) flow, the general properties of RG flows have been the subject of active research. In unitary QFTs, homoclinic RG flows are still forbidden by c, a, F theorems, but a fixed point situated in a homoclinic orbit could possibly be described by a standard CFT, in contrast to fixed points undergoing a Hopf bifurcation, and which require operators with complex scaling dimensions.
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