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Physical Review Letters

Chern-Simons-Matter Conformal Field Theory on the Fuzzy Sphere: Higgs Transition of the Kalmeyer-Laughlin Chiral Spin Liquid

Zheng Zhou, Chong Wang, Yin-Chen He

Published Jul 21, 2026• 1 citation
Publisher

Abstract

Gauge theories form a large class of interacting conformal field theories in 3D, among which critical Chern-Simons-matter theories play a prominent role. Here, we study a simple instance: a gapless complex scalar coupled to a U(1)_{2} Chern-Simons gauge field. This theory is conjectured to be dual to three other Chern-Simons-matter theories and to describe the transition between a Kalmeyer-Laughlin chiral spin liquid (a ν=1/2 bosonic Laughlin state) and a trivially gapped phase. Using the fuzzy-sphere regularization, we realize the corresponding quantum phase transition between a ν_{f}=2 fermionic integer quantum Hall state and a ν_{b}=1/2 bosonic fractional quantum Hall state. We show that the transition is continuous and governed by a conformal field theory with SO(3) global symmetry. The operator spectrum contains only one relevant Lorentz scalar, the SO(3) singlet with scaling dimension Δ_{S}=1.52(18), which tunes the transition. Our nonperturbative results identify the universality class naturally associated with the U(1)_{2} Chern-Simons-Higgs theory and show that the conjectured dualities remain self-consistent.

DOI
10.1103/m64z-bvm3

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