Confinement in QCD-like gauge theories

7 problems

• Does small-circle semiclassical confinement connect smoothly to four dimensions

  Contested

  When one space direction is curled into a small circle, confinement can be computed by hand. Whether that calculation describes the same physics as ordinary uncurled space is unknown.

• Do center vortices alone give the full SU(3) string tension

  Contested

  For two-color gluons, keeping only vortex-like defects of the field reproduces nearly all of the confining force. For three colors, as in real QCD, it is unclear whether they account for all of it.

• Does confinement imply chiral symmetry breaking in QCD-like theories

  Partially resolved

  In QCD, quark confinement comes with the spontaneous breaking of chiral symmetry (the symmetry rotating left- and right-handed quarks separately), which makes pions nearly massless. Whether confinement always forces this breaking, for any number of colors and quark types, is not proven.

• Ratio of k-string tensions in large-N Yang-Mills theory

  Open

  Heavy test charges can be grouped by how many units k of a color charge they carry that cannot be cancelled by gluons, and each k is joined by a flux string of different tension. The exact rule giving these tensions for many colors is unknown.

• Which gluon field configurations cause quark confinement

  Contested

  Computer simulations show that quarks are confined, but they do not say which shapes of the gluon field are responsible. Candidate answers include thin tubes of field (vortices) and magnetic monopoles, point-like sources of magnetic field.

• Vacuum structure of $\mathrm{SU}(2)$ Yang-Mills theory at $\theta = \pi$

  Open

  Gluon theories have a hidden angle, $\theta$; at $\theta = \pi$ a consistency argument forbids a simple featureless vacuum. For two colors it is unknown whether the vacuum splits into two mirror-image copies or does something else.

• Worldsheet theory of the confining flux tube at large N

  Open

  The tube of gluon field between quarks vibrates like a string, and lattice simulations of its vibrations show an extra particle living on the string, called the worldsheet axion. Which exact theory lives on the string as the number of colors grows is unknown.