Revisiting the φ^6 Theory in Three Dimensions at Large N

Abstract:

We investigate the O(N)--symmetric ϕ^6 theory in three spacetime dimensions using dimensional regularisation and minimal subtraction. The predictions of other methods are scrutinised in a large-NN 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.

Link to the paper:

https://arxiv.org/pdf/2502.07880