Renormalization footprints in the phase diagram of the Grosse-Wulkenhaar model

Dragan Prekrat

Published 2021-04-01Version 1

We construct and analyze a phase diagram of a self-interacting matrix field coupled to curvature of the non-commutative truncated Heisenberg space. In the infinite size limit, the model reduces to the renormalizable Grosse-Wulkenhaar's. The curvature term is crucial to renormalization. When turned off, the triple point collapses into the origin as matrices grow larger. When turned on, the triple point shifts away proportionally to the coupling strength and matrix size. Coupling attenuation that renormalizes the Grosse-Wulkenhaar model cannot contain the shifting, and the translational symmetry-breaking stripe phase escapes to infinity, taking away the problematic UV/IR mixing.