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arXiv · 1702.05749

Fixed points and the spontaneous breaking of scale invariance

Edouard Marchais·Peter Mati·Daniel F Litim
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Abstract

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. Implications for other theories are indicated.

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Edouard Marchais, Peter Mati, Daniel F Litim. 2017-02-19. Fixed points and the spontaneous breaking of scale invariance. https://doi.org/10.1103/physrevd.95.125006

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