Notes on (-2)-form symmetries
arXiv:2606.05543
The paper introduces and analyzes (-2)-form symmetries in quantum field theories via a (-1)-form symmetry of the associated Symmetry Topological Field Theory, showing how they modify the SymTFT action and relate theories with different anomaly data, and illustrates the concepts through various dimensional examples, discrete gauging constructions, and a holographic realization involving the Romans mass.
Abstract
We study -form symmetries of a -dimensional quantum field theory, via a -form symmetry of its -dimensional Symmetry Topological Field Theory (SymTFT), realized by a non-genuine codimension-one defect in the SymTFT bulk attached to a spacetime-filling topological operator. Unlike a -form symmetry of a -dimensional theory, which merely shifts a parameter of the absolute theory, a -form symmetry modifies the SymTFT action, and thereby relates theories whose ordinary global symmetries differ by anomaly data or by the associator data of a non-invertible symmetry. We illustrate the construction in two-dimensional toy models, three-dimensional ABJM-type theories, four-dimensional generalized Yang--Mills theory, and in a fusion-categorical example relating the non-invertible symmetries and . We then develop a club-sandwich realization, in which a quarter-gauging operation interfaces between IR phases of distinct RG flows of a common UV theory, and an alternative realization via nested discrete gauging. Finally, we present a holographic, top-down realization in which the type IIA Romans mass plays the role of a -form background for a three-dimensional Chern--Simons-matter theory, with shifts of the Romans mass realizing shifts of the boundary anomaly coefficients. We also discuss related constructions for coupled bulk--boundary systems.
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