Matching higher symmetries across Intriligator-Seiberg duality

TL;DR

The paper analyzes higher symmetries and their 't Hooft anomalies in 4d $\mathfrak{so}(2n_c)$ gauge theories with $2n_f$ flavors, emphasizing how parity, global gauge form, and a discrete theta angle shape the $0$-form and $1$-form symmetry mixing into 2-groups. It develops a detailed line-operator analysis to classify when the $1$-form and flavor symmetries extend nontrivially or exhibit anomalies, and uses an $\mathrm{SL}(2,\mathbb{Z}_2)$ framework to track anomalies under dualities. Fermion zero modes around monopoles are shown to drive these anomaly structures, with explicit results for all parity combinations $(n_c,n_f) \in \{(\text{even},\text{even}), (\text{odd},\text{even}), (\text{even},\text{odd}), (\text{odd},\text{odd})\}$. The Intriligator-Seiberg duality is checked against these 2-group and anomaly structures, confirming consistent duality mappings like $\mathrm{Spin}(2n_c) \leftrightarrow T(\mathrm{SO}_-(2n_f-2n_c+4))$ and preserving the four-type behavior across dual pairs. Overall, the work provides a field-theoretic account of higher symmetries in SO QCDs and connects them robustly to duality structures, with potential implications for SUSY and beyond.

Abstract

We study higher symmetries and anomalies of 4d $\mathfrak{so}(2n_c)$ gauge theory with $2n_f$ flavors. We find that they depend on the parity of $n_c$ and $n_f$, 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 $\mathfrak{so}(2n_c)\leftrightarrow\mathfrak{so}(2n_f-2n_c+4)$.