On the negative coupling O(N) model in 2d at high temperature

Paul Romatschke

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arXiv · 2412.10496

On the negative coupling O(N) model in 2d at high temperature

Paul Romatschke

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Abstract

In this work, I consider N-component scalar quantum field theory in two dimensions interacting with an upside-down quartic potential. Working in the large N limit, the model can be solved non-perturbatively using the saddle-point method for sufficiently strong negative coupling. At high temperature, the O(N) model dimensionally reduces to ${\cal PT}$-symmetric quantum mechanics, for which powerful non-perturbative solution methods exist. It is found that the solution from quantum mechanics can be matched by the saddle-point method in quantum field theory when allowing for saddles beyond the principal Riemann sheet. I show that saddle points on non-principal Riemann sheets lead to a fully consistent solution of the 2d negative-coupling O(N) model for all temperatures.

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Paul Romatschke. 2024-12-13. On the negative coupling O(N) model in 2d at high temperature. https://arxiv.org/abs/2412.10496

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