Irreversibility of the renormalization group flow in non-unitary quantum field theory
Abstract
We show irreversibility of the renormalization group flow in non-unitary but -invariant quantum field theory in two space-time dimensions. In addition to unbroken -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 -theorem to -symmetric hamiltonians. Our proof follows closely Zamolodchikov's arguments. We show that a function of the renormalization group parameter exists which is non-negative 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 , where is the central charge and is the lowest primary field dimension in the conformal field theory which describes the critical point.
Keywords
Cite
@article{arxiv.1706.01871,
title = {Irreversibility of the renormalization group flow in non-unitary quantum field theory},
author = {Olalla A. Castro-Alvaredo and Benjamin Doyon and Francesco Ravanini},
journal= {arXiv preprint arXiv:1706.01871},
year = {2017}
}
Comments
26 pages, 1 figure