Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
On gauging Abelian extensions of finite and U(1) groups
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abstract
We consider Abelian extensions of global symmetries of the form $A \to G \to K$, with $A$ finite. For a quantum field theory $\mathcal{T}$ with symmetry $G$, we compare gauging $G$ directly with gauging first $A$ and then $K$, and show that for finite Abelian groups and for $K \simeq U(1)$ the two procedures are equivalent as expected, $\mathcal{T}/G \simeq \mathcal{T}/A/K$. In the continuous case $K=U(1)$, after gauging the full extension, the dual symmetry $\widehat{\mathbb{Z}}_q^{(d-2)}$ fits into an extension characterizing the topological data of the magnetic $U(1)_m^{(d-3)}$ symmetry. This is better described using differential cohomology.
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Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.
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Half-Spacetime Gauging of 2-Group Symmetry in 3d
Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
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Gauging in superconductors and other electronic systems
Superconductors are bosonic at low energy yet carry a gravito-magnetic anomaly from fermion parity gauging that forbids trivial massive phases in 3D and 4D.