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Title
Discrete gauge anomalies and instantons
KIAS Author
Yi, Piljin,Jia, Qiang
Journal
JOURNAL OF HIGH ENERGY PHYSICS, 2024
Archive
Hep-th/2405.09007
Abstract
We revisit anomalous phases related to large gauge transformations, such as the Witten anomaly. The latter, known to plague d = 4 Sp(k) theories, is well-understood in terms of pi 4(Sp(k)) = Z(2), but it also has an oblique relation to the instantons, labeled by pi 3(G) = Z, via the fermion zero mode counting. We revisit this relation and point out how SU(N) theories escape an anomalous sign of the latter type, only thanks to the perturbative anomaly cancelation condition that restricts the chiral fermion spectrum. This leads to the question of what happens if the latter, more mundane anomaly is canceled by an inflow instead. After raising an open question about fractional D3 probe theories, we explore the simplest bottom-up model of such a kind, due to Witten and Yonekura, from which we find the relevant chiral theories to be free of such a disease despite the unrestricted chiral spectra. We close with a simple but often-overlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in d = 3.