From QED$_3$ to Self-Dual Multicriticality in the Fradkin-Shenker Model

• URL: http://arxiv.org/abs/2602.23420v1
• Date: Thu, 26 Feb 2026 19:00:00 GMT
• Title: From QED$_3$ to Self-Dual Multicriticality in the Fradkin-Shenker Model
• Authors: Thomas T. Dumitrescu, Pierluigi Niro, Ryan Thorngren,
• Abstract summary: We consider the Fradkin-Shenker $mathbb Z$ gauge-Higgs lattice model in 2+1 dimensions.<n>Its phase diagram contains a multicritical CFT with gapless, mutually non-local electric and magnetic particles.<n>We compute the scaling dimensions of some operators using a large-$N_f$ expansion and find agreement with the emergent selection rules.
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• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: We consider the Fradkin-Shenker ${\mathbb Z}_2$ gauge-Higgs lattice model in 2+1 dimensions, i.e. the toric code deformed by an in-plane magnetic field. Its phase diagram contains a multicritical CFT with gapless, mutually non-local electric and magnetic particles, exchanged by a ${\mathbb Z}_2^{\mathsf{D}}$ self-duality symmetry. We introduce a staggered generalization of the model in which these particles carry global $U(1)_e$ and $U(1)_m$ charges, respectively, and we propose a continuum QFT description in terms of QED$_3$ with $N_f = 2$ Dirac fermion flavors and a charge-two Higgs field with Yukawa couplings. The conjectured phase diagram harbors a multicritical CFT with $(O(2)_e \times O(2)_m)\rtimes\mathbb{Z}_2^\mathsf{D}$ symmetry, some of which is emergent in the QFT description. We compute the scaling dimensions of some operators using a large-$N_f$ expansion and find agreement with the emergent selection rules. The staggered model admits a deformation to the original Fradkin-Shenker model, which maps to unit-charge monopole operators in Higgs-Yukawa-QED$_3$ that break the $U(1)_e \times U(1)_m$ symmetry. We show explicitly that this deformation reproduces all features of the Fradkin-Shenker phase diagram. Finally, we propose a multicritical duality between Higgs-Yukawa-QED$_3$ and the easy-plane $\mathbb{ CP}^1$ model (i.e. two-flavor scalar QED$_3$ with a suitable potential), which describes spin-1/2 anti-ferromagnets on a square lattice. This duality implies a first-order line of Néel-VBS transitions ending in a deconfined quantum multicritical point, described by the same $O(2)_e \times O(2)_m$ symmetric CFT that arises in the staggered Fradkin-Shenker model, which separates it from a gapped ${\mathbb Z}_2$ spin liquid phase.

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