On the Light dilaton in the Large N Tri-critical O(N) Model

TL;DR

This paper investigates the large N limit of the three-dimensional O(N) phi-six theory, revealing that the expected light dilaton in the spontaneously broken phase is actually a tachyon, indicating an instability.

Contribution

It demonstrates that the light dilaton predicted at next-to-leading order is a tachyon, challenging the stability of the phase with broken scale invariance.

Findings

The light dilaton is a tachyon, indicating instability.

Spontaneous scale symmetry breaking leads to a tachyonic mode.

The phase with broken scale invariance is unstable.

Abstract

The leading order of the large N limit of the O(N) symmetric phi-six theory in three dimensions has a phase which exhibits spontaneous breaking of scale symmetry accompanied by a massless dilaton which is a Goldstone boson. At the next-to-leading order in large N, the phi-six coupling has a beta function of order 1/N and it is expected that the dilaton acquires a small mass, proportional to the beta function and the condensate. In this note, we show that this "light dilaton" is actually a tachyon. This indicates an instability of the phase of the theory with spontaneously broken approximate scale invariance.