Abstract
We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry. We canonically quantize on \U0001d54b3, in a fixed background field gauging the 1-form symmetry. We show that the mixed 0-form/1-form ’t Hooft anomaly results in a central extension of the global-symmetry operator algebra. We determine this algebra in each case and show that the anomaly implies degeneracies in the spectrum of the Hamiltonian at any finite- size torus. We discuss the consistency of these constraints with both older and recent semiclassical calculations in SU(N) theories, with or without adjoint fermions, as well as with their conjectured infrared phases.
Highlights
The anomaly matching conditions of ’t Hooft offer an important consistency check on possible scenarios for the nonperturbative behaviour of gauge theories [1]
We study four-dimensional gauge theories with arbitrary simple gauge group with 1-form global center symmetry and 0-form parity or discrete chiral symmetry
A related example [4] is the mixed anomaly between discrete chiral symmetry and center symmetry in super Yang-Mills theory, present in
Summary
The anomaly matching conditions of ’t Hooft offer an important consistency check on possible scenarios for the nonperturbative behaviour of gauge theories [1]. We shall show that 4d gauge theories with a mixed discrete 0-form/1-form anomaly give rise to a centrally-extended symmetry algebra. An indication for this has been seen before: on R3 × S1, using the semiclassical solution of deformed SU(N ) Yang-Mills. The doubledegeneracy at θ = π, exactly as implied by the centrally-extended algebra, was seen in semiclassical calculations of the instanton-induced splitting of ’t Hooft electric flux energies in the background twisted by m, in the framework of the “femto-universe,” where the entire T3 is taken smaller than Λ−1. Some possible venues for future studies are discussed in the text
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