Abstract
We study higher symmetries and anomalies of 4d mathfrak{so} (2nc) gauge theory with 2nf flavors. We find that they depend on the parity of nc and nf, the global form of the gauge group, and the discrete theta angle. The contribution from the fermions plays a central role in our analysis. Furthermore, our conclusion applies to mathcal{N} = 1 supersymmetric cases as well, and we see that higher symmetries and anomalies match across the Intriligator-Seiberg duality between mathfrak{so} (2nc) ↔ mathfrak{so} (2nf − 2nc + 4).
Highlights
Mixed anomalies between them, or they can combine nontrivially to form a symmetry structure called 2-groups
We study higher symmetries and anomalies of 4d so(2nc) gauge theory with 2nf flavors
We find that they depend on the parity of nc and nf, the global form of the gauge group, and the discrete theta angle
Summary
We first determined the 2-group structure in section 2 by studying the charges of line operators, and determined the anomalies in section 3 by matching it to the action of SL(2, Z2). Since the 1-form symmetry background in the Spin theory is the Stiefel-Whitney class w2 of the SO(2nc) gauge bundle, these anomalies should come from the anomalies of fermions charged under. As such, this cochain still affects the gauging process. This cochain still affects the gauging process The aim of this last section is to give a check of these anomalies from a different point of view. Witten theory, which was more recently recognized as determining an anomaly in [10, section 2.4.3]. It was used in [44, section 3.1 and 5.1.2] to relate the ‘new’ SU(2). In a couple of cases we can say more, as we comment along the way
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