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

Abstract

We investigate the $O(N)$--symmetric ${\varphi }^6$ 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 $N\to \infty$ 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 $1/N$-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 $N$.

arXiv comment16 pages, 5 figures. v2: match publication

References in corpus (15)

• FORM version 4.0
• Asymptotic safety guaranteed
• Vacuum stability of asymptotically safe gauge-Yukawa theories
• Derivative expansion of the renormalization group in O(N) scalar field theory
• Feynman Diagrams to Three Loops in Three Dimensional Field Theory
• Seeking Fixed Points in Multiple Coupling Scalar Theories in the $\epsilon$ Expansion
• Surprises in the $O(N)$ models: nonperturbative fixed points, large $N$ limit and multi-criticality
• Fixed points and the spontaneous breaking of scale invariance
• Critical $O(N)$ models in the complex field plane
• Asymptotic safety with Majorana fermions and new large N equivalences
• Asymptotic safety of scalar field theories
• On the Light dilaton in the Large N Tri-critical O(N) Model
• Application of the DRA method to the calculation of the four-loop QED-type tadpoles
• The finite $N$ origin of the Bardeen-Moshe-Bander phenomenon and its extension at $N=\infty$ by singular fixed points
• Study of the Ultraviolet Behavior of an O($N$) $|\vec{\varphi }{|}^6$ Theory in $d=3$ Dimensions