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arXiv · 2110.07617

Convexity, large charge and the large-N phase diagram of the $\varphi^4$ theory

Rafael Moser·Domenico Orlando·Susanne Reffert
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Abstract

In this note we discuss the phase space of the O(2N) vector model in the presence of a quadratic and a quartic interaction by writing the large-N effective potential using large charge methods in dimensions 2<D<4 and 4<D<6. Based on a simple discussion of the convexity properties of the grand potential, we find very different behavior in the two regimes: while in 2<D<4, the theory is well-behaved, the model in 4<D<6 leads to a complex CFT in the UV, consistently with earlier results. We also find a new metastable massive phase in the high-energy regime for the theory on the cylinder.

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Rafael Moser, Domenico Orlando, Susanne Reffert. 2021-10-14. Convexity, large charge and the large-N phase diagram of the $\varphi^4$ theory. https://doi.org/10.1007/jhep02(2022)152

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