Abstract
We study higher-form symmetries in 5d quantum field theories, whose charged operators include extended operators such as Wilson line and ’t Hooft operators. We outline criteria for the existence of higher-form symmetries both from a field theory point of view as well as from the geometric realization in M-theory on non-compact Calabi-Yau threefolds. A geometric criterion for determining the higher-form symmetry from the intersection data of the Calabi-Yau is provided, and we test it in a multitude of examples, including toric geometries. We further check that the higher-form symmetry is consistent with dualities and is invariant under flop transitions, which relate theories with the same UV-fixed point. We explore extensions to higher-form symmetries in other compactifications of M-theory, such as G2-holonomy manifolds, which give rise to 4d mathcal{N} = 1 theories.
Highlights
Higher-form symmetries [1] generalize ordinary symmetries, and have played an important role in uncovering refined properties of quantum field theories
The field theoretic approach is complemented with an analysis in M-theory, where we find a geometric characterization of the 1-form symmetry in terms of the intersection theory on the non-compact Calabi-Yau threefold
We provide evidence for this by determining the higher-form symmetries in 6d for the building blocks, namely the non-Higgsable clusters (NHCs) and conformal matter theories, and find agreement with the 1-form symmetry in 5d computed by intersection theory in the resolved Calabi-Yau threefold
Summary
Higher-form symmetries [1] generalize ordinary symmetries, and have played an important role in uncovering refined properties of quantum field theories. The field theoretic approach is complemented with an analysis in M-theory, where we find a geometric characterization of the 1-form symmetry in terms of the intersection theory on the non-compact Calabi-Yau threefold This is shown to agree with the 1-form symmetry computed from the gauge theory description, whenever such a formulation exists, but is applicable more generally, e.g., to the rank one P2 theory, which we show to have a Z3 1-form symmetry. The quotient group in (1.1) can be straightforwardly computed from the intersection matrix of compact divisors and compact curves in M6, which we use to determine it in many examples This point of view allows generalization to other M-theory compactifications such as higher dimensional Calabi-Yau manifolds and G2 and Spin(7) holonomy spaces. While we were completing this paper we were informed of related work to appear in [13] after one of us presented our results in [14]
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