Lower edge of the conformal window in SU(3) gauge theory
In plain words
QCD with many massless quark species becomes scale invariant at long distances. The smallest number of species for which this happens is unknown.
Precise statement
$\mathrm{SU}(3)$ gauge theory with $N_{f}$ massless Dirac fermions in the fundamental representation is asymptotically free for $N_{f} < 16.5$ and has a perturbative IR fixed point near that value. Determine $N_{f}^{*}$ such that for $N_{f}^{*} \le N_{f} < 16.5$ the IR is a CFT and for smaller $N_{f}$ chiral symmetry breaks; in particular decide $N_{f} = 8, 10 \text{ and } 12$.
What would settle it
Continuum-extrapolated lattice determinations of the step-scaling function or spectrum for $N_f = 8\ \text{to}\ 13$ that agree between independent groups.
Status in the literature
Unverified note: it names recent work and was partly written without a live literature search; it awaits a check by an editor.
Lattice groups disagree on $N_{f} = 10\text{ and }12$; estimates of $N_{f}^{*}$ range from about 9 to 13 (2009-2025).
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See also
- Related Does confinement imply chiral symmetry breaking in QCD-like theories?
- Related Do complex fixed points explain the pseudocritical drift at deconfined transitions?
- Related Is the Higgs boson elementary or a composite bound state?
- Related Infrared phase of SU(2) gauge theory with two adjoint Weyl fermions
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