Conformal bootstrap, critical points and conformal windows

6 problems

• Infrared phase of SU(2) gauge theory with two adjoint Weyl fermions

  Contested

  A close relative of QCD, with matter particles of a different type, has several candidate behaviors at long distances. Which one it chooses is unknown.

• Does an interacting unitary O(N) CFT exist in five dimensions

  Contested

  In five dimensions, a model of N-component spins may have a scale-invariant point that appears only at short distances. Whether this point is a consistent quantum theory for realistic N is unknown.

• Helium $\lambda$-point heat-capacity exponent disagrees with theory

  Contested

  The heat capacity of liquid helium near its superfluid transition was measured in orbit with high precision. Its critical exponent disagrees with the theoretical value by many error bars.

• Do non-supersymmetric conformal manifolds exist above two dimensions

  Contested

  Some scale-invariant theories come in continuous families, in which a parameter can be changed while scale invariance stays exact. Above two dimensions, all established interacting examples rely on supersymmetry, a symmetry between bosons and fermions, and whether any exist without it is unknown.

• Critical flavor number for chiral symmetry breaking in QED3

  Contested

  Electrodynamics in two space dimensions with N species of massless electrons is scale invariant at long distances when N is large. Below which N this fails is unknown.

• Lower edge of the conformal window in SU(3) gauge theory

  Contested

  QCD with many massless quark species becomes scale invariant at long distances. The smallest number of species for which this happens is unknown.