2026/07/22 by Yasin F. Alam, Andreas Karch, Da-Chuan Lu +1
#hep-th #cond-mat.str-el
The SL(2,ℤ) electromagnetic duality of 4d Maxwell theory induces theory-generating operations on 3d theories with U(1) global symmetry. For theories with U(1)n symmetry, this structure generalizes to Sp(2n,ℤ). Focusing on the U(1)2 case, we formulate the bulk Sp(4,ℤ) action and derive the corresponding boundary operations. We identify an intrinsically two-component element of order five, which generalizes the order-three ST element of the single-U(1) theory. Although its fifth power acts trivially in the bulk, the corresponding boundary operation closes only up to a decoupled U(1)1 invertible phase, suggesting a mixed duality-gravitational anomaly. We realize the resulting theory-generating web for Abelian Chern-Simons theories within the K-matrix formalism and apply it to bilayer fractional quantum Hall systems. Recasting the Haldane--Halperin hierarchy construction as a sequence of SL(2,ℤ) operations, we generalize it to systems with charge U(1)c and pseudospin U(1)s symmetries. The resulting bilayer hierarchies contain branches terminating in an interlayer-correlated bosonic (221) daughter sector, yielding candidate Abelian states at the even-denominator equal-layer fillings 3/8+3/8 and 5/12+5/12. Integral changes of anyon basis establish the equivalence of these states to their corresponding Abelian composite-fermion descriptions. We further discuss the spin-charge constraints that arise when the electromagnetic background field is treated as a spin-c connection.