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

High Energy Physics - Theory 2017-12-08 v1 Statistical Mechanics Mathematical Physics math.MP

Abstract

We show irreversibility of the renormalization group flow in non-unitary but PT{\cal PT}-invariant quantum field theory in two space-time dimensions. In addition to unbroken PT\mathcal{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 cc-theorem to PT{\cal PT}-symmetric hamiltonians. Our proof follows closely Zamolodchikov's arguments. We show that a function ceff(s)c_{\mathrm{eff}}(s) of the renormalization group parameter ss 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 ceff=c24Δc_{\mathrm{eff}}=c-24\Delta, where cc is the central charge and Δ\Delta 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