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arXiv · 2211.15683

A solvable quantum field theory with asymptotic freedom in 3+1 dimensions

Paul Romatschke
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Abstract

Recently, Ai, Bender and Sarkar gave a prescription on how to obtain $\mathcal{PT}$-symmetric field theory results from an analytic continuation of Hermitian field theories. I perform this analytic continuation for the massless (critical) O(N) model with quartic interaction in 3+1 dimensions. In the large N limit, this theory is exactly solvable, and has negative $\beta$-function in the ultraviolet, and a stable bound state in the infrared. The coupling diverges at a scale $\Lambda_c$, but can be continued into the far infrared. At finite temperature, the theory exhibits two phases separated by a second-order phase transition near $T_c\simeq \Lambda_c/\sqrt{e}$.

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Paul Romatschke. 2022-11-28. A solvable quantum field theory with asymptotic freedom in 3+1 dimensions. https://arxiv.org/abs/2211.15683

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