Revisiting the ${\phi }^6$ Theory in Three Dimensions at Large $N$

We investigate the $O(N)$–symmetric ${\phi }^6$ theory in three spacetime dimensions using dimensional regularisation and minimal subtraction. The predictions of other methods are scrutinised in a large-$N$ expansion. We show how the tricritical line of fixed point emerges in a strict $N\to \mathrm{\infty }$ 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 $1\mathrm{/}N$-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 $N$.