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.

• Received 8 June 2018

DOI:https://doi.org/10.1103/PhysRevD.98.034026

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Published by the American Physical Society