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<p>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 <InlineEquation ID="IEq1"> <InlineMediaObject> <ImageObject Color="BlackWhite" FileRef="13130_2025_25886_Article_IEq1.gif" Format="GIF" Height="14" Rendition="HTML" Resolution="72" Type="Linedraw" Width="27" /> </InlineMediaObject> <EquationSource Format="MATHML"><math display="inline"> <mi mathvariant="script">PT</mi> </math></EquationSource> <EquationSource Format="TEX">\( \mathcal{PT} \)</EquationSource> </InlineEquation>-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.</p>

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

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  • 发表日期：

    2025年4月1日

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  • Paul Romatschke

摘要

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 PT \( \mathcal{PT} \) -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.