Discrete Gauge Anomalies and Instantons
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 wellunderstood in terms of $\pi_4(Sp(k))=\mathbb{Z}_2$, but it also has an oblique relation to the instantons, labeled by $\pi_3(G)=\mathbb{Z}$, 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 bottomup 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 oftenoverlooked observation about how fermionic zero modes enter physics differently between Euclidean and Lorentzian descriptions and point out a related issue in $d=3$.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.09007
 arXiv:
 arXiv:2405.09007
 Bibcode:
 2024arXiv240509007J
 Keywords:

 High Energy Physics  Theory
 EPrint:
 39 pages, 7 figures