Abstract
We study the discrete chiral- and center-symmetry ’t Hooft anomaly matching in the charge-q two-dimensional Schwinger model. We show that the algebra of the discrete symmetry operators involves a central extension, implying the existence of q vacua, and that the chiral and center symmetries are spontaneously broken. We then argue that an axial version of the q = 2 model appears in the worldvolume theory on domain walls between center-symmetry breaking vacua in the high-temperature SU(2) \( \mathcal{N}=1 \) super-Yang-Mills theory and that it inherits the discrete ’t Hooft anomalies of the four-dimensional bulk. The Schwinger model results suggest that the high-temperature domain wall exhibits a surprisingly rich structure: it supports a non-vanishing fermion condensate and perimeter law for spacelike Wilson loops, thus mirroring many properties of the strongly coupled four-dimensional low-temperature theory. We also discuss generalizations to theories with multiple adjoint fermions and possible lattice tests.
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Anber, M.M., Poppitz, E. Anomaly matching, (axial) Schwinger models, and high-T super Yang-Mills domain walls. J. High Energ. Phys. 2018, 76 (2018). https://doi.org/10.1007/JHEP09(2018)076
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DOI: https://doi.org/10.1007/JHEP09(2018)076