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Irreversibility of the renormalization group flow in non-unitary quantum field theory

Castro-Alvaredo, O., Doyon, B. & Ravanini, F. (2017). Irreversibility of the renormalization group flow in non-unitary quantum field theory. Journal of Physics A: Mathematical and Theoretical, 50(42), article number 424002. doi: 10.1088/1751-8121/aa8a10


We show irreversibility of the renormalization group flow in non-unitary but PT -invariant quantum field theory in two space-time dimensions. In addition to unbroken PT -symmetry and a positive energy spectrum, we assume standard properties of quantum field theory including a local energy-momentum tensor and relativistic invariance. This generalizes Zamolodchikov’s ctheorem to PT -symmetric hamiltonians. Our proof follows closely Zamolodchikov’s arguments. We show that a function ceff(s) of the renormalization group parameter s exists which is nonnegative and monotonically decreasing along renormalization group flows. Its value at a critical point is the “effective central charge” entering the specific free energy. At least in rational models, this equals ceff = c − 24∆, where c is the central charge and ∆ is the lowest primary field dimension in the conformal field theory which describes the critical point.

Publication Type: Article
Additional Information: This is an author-created, un-copyedited version of an article accepted for publication/published in Journal of Physics A: Mathematical and Theoretical. IOP Publishing Ltd is not responsible for any errors or omissions in this version of the manuscript or any version derived from it. The Version of Record is available online at
Publisher Keywords: Renormalization group flows, c-function, non-unitary conformal field theory, non-unitary quantum field theory
Departments: School of Science & Technology > Mathematics
SWORD Depositor:
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