Two-flavor adjoint QCD

Understand

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 $\mathbb R^4$ 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.