1,370 research outputs found
Walking, Weak first-order transitions, and Complex CFTs II. Two-dimensional Potts model at
We study complex CFTs describing fixed points of the two-dimensional
-state Potts model with . Their existence is closely related to the
weak first-order phase transition and walking RG behavior present in the real
Potts model at . The Potts model, apart from its own significance, serves
as an ideal playground for testing this very general relation. Cluster
formulation provides nonperturbative definition for a continuous range of
parameter , while Coulomb gas description and connection to minimal models
provide some conformal data of the complex CFTs. We use one and two-loop
conformal perturbation theory around complex CFTs to compute various properties
of the real walking RG flow. These properties, such as drifting scaling
dimensions, appear to be common features of the QFTs with walking RG flows, and
can serve as a smoking gun for detecting walking in Monte Carlo simulations.
The complex CFTs discussed in this work are perfectly well defined, and can
in principle be seen in Monte Carlo simulations with complexified coupling
constants. In particular, we predict a pair of -symmetric complex CFTs
with central charges describing the fixed points
of a 5-state dilute Potts model with complexified temperature and vacancy
fugacity.Comment: 34 pages, 13 figures. v2: refs added; v3 refs added, typos corrected,
presentation of several arguments clarifie
Flux Tube Spectra from Approximate Integrability at Low Energies
We provide a detailed introduction to a method we recently proposed for
calculating the spectrum of excitations of effective strings such as QCD flux
tubes. The method relies on the approximate integrability of the low energy
effective theory describing the flux tube excitations and is is based on the
Thermodynamic Bethe Ansatz (TBA). The approximate integrability is a
consequence of the Lorentz symmetry of QCD. For excited states the convergence
of the TBA technique is significantly better than that of the traditional
perturbative approach. We apply the new technique to the lattice spectra for
fundamental flux tubes in gluodynamics in D=3+1 and D=2+1, and to k-strings in
gluodynamics in D=2+1. We identify a massive pseudoscalar resonance on the
world sheet of the confining strings in SU(3) gluodynamics in D=3+1, and
massive scalar resonances on the world sheet of k=2,3 strings in SU(6)
gluodynamics in D=2+1.Comment: 44 pages, 19 figures, v2: references added, to appear in special
issue of JETP dedicated to Valery Rubakov's 60th birthda
Walking, Weak first-order transitions, and Complex CFTs
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.Comment: 38 pages, added reference
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