Revisiting the ϕ6 theory in three dimensions at large N

Abstract

We investigate the O (N)-symmetric ϕ6 theory in three spacetime dimensions using dimensional regularization and minimal subtraction. The predictions of other methods are scrutinized in a large-N expansion. We show how the tricritical line of fixed point emerges in a strict N → ∞ limit but argue that it is not a physical manifestation. For the first time in this explicit manner, we compute the effective potential at next-to-leading order in the 1/N-expansion and discuss its stability. The Bardeen-Moshe-Bander phenomenon is also analysed at next-to-leading order, and we demonstrate that it disappears without breaking the scale invariance spontaneously. Our findings indicate that the UV fixed point found by Pisarski persists at large N.