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Non-invertible self-duality defects of Cardy-Rabinovici model and mixed gravitational anomaly
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abstract
We study properties of self-duality symmetry in the Cardy-Rabinovici model. The Cardy-Rabinovici model is the $4$d $U(1)$ gauge theory with electric and magnetic matters, and it enjoys the $SL(2,\mathbb{Z})$ self-duality at low-energies. $SL(2,\mathbb{Z})$ self-duality does not realize in a naive way, but we notice that the $ST^{p}$ duality transformation becomes the legitimate duality operation by performing the gauging of $\mathbb{Z}_N$ $1$-form symmetry with including the level-$p$ discrete topological term. Due to such complications in its realization, the fusion rule of duality defects becomes a non-group-like structure, and thus the self-duality symmetry is realized as a non-invertible symmetry. Moreover, for some fixed points of the self-duality, the duality symmetry turns out to have a mixed gravitational anomaly detected on a $K3$ surface, and we can rule out the trivially gapped phase as a consequence of anomaly matching. We also uncover how the conjectured phase diagram of the Cardy-Rabinovici model satisfies this new anomaly matching condition.
Forward citations
Cited by 4 Pith papers
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$\mathrm{SL}(2,\mathbb{Z})$ Theta Subgroup Structure of Maxwell theory in the Lattice Villain Hamiltonian Formulation
Lattice Villain Maxwell theory realizes the theta subgroup of SL(2,Z) via Hamiltonian operators S and T2, with charge exchange, the Witten effect, and a non-invertible defect with Tambara-Yamagami fusion.
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Non-invertible translation from Lieb-Schultz-Mattis anomaly
Gauging the full internal symmetry of a lattice system with an LSM anomaly turns lattice translation into a non-invertible operator whose fusion rules involve condensation defects.
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2d Cardy-Rabinovici model with the modified Villain lattice: Exact dualities and symmetries
The 2d Cardy-Rabinovici model is constructed on a modified Villain lattice, making rescaled theta periodicity and strong-weak duality exact at finite spacing and giving a symmetry-based phase classification.
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The Higher Structure of Symmetries of Axion-Maxwell Theory
The paper determines the fusion interfaces and F-symbols for the non-invertible electric 1-form symmetry of 4d axion-Maxwell theory.
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