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A solvable quantum field theory with asymptotic freedom in 3+1 dimensions
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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 $T_c\simeq \Lambda_c/\sqrt{e}$.
Forward citations
Cited by 2 Pith papers
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On the negative coupling O(N) model in 2d at high temperature
For the 2d negative-coupling O(N) model at large N, the correct vacuum is a saddle point on a non-principal Riemann sheet, giving a real free energy and dynamical stability at all temperatures.
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Oscillators with imaginary coupling: spectral functions in quantum mechanics and quantum field theory
A pair of oscillators or scalar fields with imaginary coupling has real energy levels under a modified inner product, and non-positive spectral functions are linked to non-observable operators.
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