Lattice definition of chiral gauge theories

4 problems

• Infrared phase of strongly coupled chiral gauge theories

  Open

  Theories where left and right particles feel the force differently can become strongly interacting at long distances. Whether they then confine with massless composite particles or break their symmetries is unknown.

• Can interactions decouple mirror fermions in lattice chiral theories

  Contested

  Grid versions of fermions come with unwanted partner particles of opposite handedness, called mirror fermions. The proposal is to make the mirrors heavy with strong interactions and leave the wanted particles massless.

• Gauge-invariant lattice definition of nonabelian chiral gauge theories

  Open

  A grid version exists for chiral theories with the simplest, electromagnetism-like forces. For the non-commuting forces of the Standard Model it is still missing.

• Continuous symmetric mass generation for sixteen Weyl fermions in 4D

  Contested

  Particles normally get mass by breaking a symmetry. The question is whether strong interactions can give mass to sixteen massless fermions in four dimensions while every symmetry is kept, through a smooth (continuous) change from the massless phase.