Infrared phase of strongly coupled chiral gauge theories
In plain words
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.
Precise statement
For asymptotically free 4D chiral gauge theories such as SU(5) with fermions in 5bar + 10, or the Bars-Yankielowicz and Georgi-Glashow families, determine the infrared phase: confinement with massless composite fermions saturating 't Hooft anomalies, dynamical Higgsing (tumbling, color-flavor locking), or an IR CFT.
What would settle it
Nonperturbative simulation of the theory, which requires a lattice chiral regularization, or anomaly arguments that exclude all but one phase.
Status in the literature
Unverified note
Generalized-anomaly arguments (2019-2025) constrain but do not fix the phase.