Two-flavor adjoint QCD

We study four-dimensional $SU(2)$ Yang-Mills theory with two massless adjoint Weyl fermions. When compactified on a spatial circle of size L much smaller than the strong-coupling scale, this theory can be solved by weak-coupling nonperturbative semiclassical methods. We study the possible realizations of symmetries in the R⁴ limit and find that all continuous and discrete 0-form and 1-form 't Hooft anomaly-matching conditions are saturated by a symmetry realization and massless spectrum identical to that found in the small-L limit, with only a single massless flavor-doublet fermion in the infrared. This observation raises the possibility that the class of theories which undergo no phase transition between the analytically solvable small-size circle and strongly coupled infinite-size circle is larger than previously thought and offers new challenges for lattice studies.