2025/04/12 by André LeClair, LeClair, André
Physics and Astronomy · #Cosmology and Gravitation Theories #FOS: Physical sciences #High Energy Physics - Phenomenology (hep-ph) #High Energy Physics - Theory (hep-th) #Particle physics theoretical and experimental studies #Quantum Chromodynamics and Particle Interactions
paper · pdf · doi:10.48550/arxiv.2504.09327
openalex publication_date 2025/04/12 · openalex created_date 2025/10/14 · openalex updated_date 2026/08/02
We define a model of 2 coupled SU(2) doublets of scalar fields in 4 spacetime dimensions which have a rich structure of renormalization group (RG) flows to 1-loop when the SU(2) is broken to U(1). The model is pseudo-hermitian, H^† = \cal K H \cal K^† with \cal K ^† \cal K = \cal K2 =1, which makes it non-unitary, however in a very specific manner with some desirable properties. We compute the beta functions to 3 loops from the operator product expansion and show that the 1-loop structure of flows persists to higher orders. For SU(2) broken to U(1), we conjecture a beta function to all orders. The flows can be extended to large coupling using a strong-weak coupling symmetry g → 1/g of the beta functions. One finds a line of fixed points which are non-unitary conformal field theories in 4 spacetime dimensions that were previously unknown. We also find massless flows between 2 non-trivial fixed points, and a regime with a cyclic RG flow, which is allowed since the model is non-unitary. For the flows between fixed points on the critical line, we compute the anomalous dimensions of the perturbations in the UV and IR, and identify some special points where anomalous dimensions are rational numbers.