Walking, Weak first-order transitions, and Complex CFTs
Résumé
We discuss walking behavior in gauge theories and weak first-order phase transitions in statistical physics. Despite appearing in very different systems (QCD below the conformal window, the Potts model, deconfined criticality) these two phenomena both imply approximate scale invariance in a range of energies and have the same RG interpretation: a flow passing between pairs of fixed point at complex coupling. We discuss what distinguishes a real theory from a complex theory and call these fixed points complex CFTs. By using conformal perturbation theory we show how observables of the walking theory are computable by perturbing the complex CFTs. This paper discusses the general mechanism while a companion paper [1] will treat a specific and computable example: the two-dimensional Q-state Potts model with Q > 4. Concerning walking in 4d gauge theories, we also comment on the (un)likelihood of the light pseudo-dilaton, and on non-minimal scenarios of the conformal window termination.
Mots clés
Conformal Field Theory
Renormalization Group
Lattice Quantum Field Theory
field theory: conformal
coupling: complex
dimension: 2
gauge field theory
Potts model
fixed point
quantum chromodynamics
renormalization group
perturbation theory
critical phenomena
deconfinement
nonminimal
dilaton
scaling
flow