Fixed points and the spontaneous breaking of scale invariance

Understand

We investigate critical $N$-component scalar field theories and the spontaneous breaking of scale invariance in three dimensions using functional renormalisation.

• Global and local renormalisation group flows are solved analytically in the infinite $N$ limit to establish the phase diagram including the Wilson-Fisher fixed point and a line of asymptotically safe UV fixed points characterised by an exactly marginal sextic coupling.
• We also study the Bardeen-Moshe-Bander phenomenon of spontaneously broken scale invariance and the stability of the vacuum for general regularisation.
• Our findings clarify a long-standing puzzle about the apparent unboundedness of the effective potential.