SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement

Abstract

We study gapless phases in (3+1)d in the presence of 1-form and non-invertible duality symmetries. Using the Symmetry Topological Field Theory (SymTFT) approach, we classify the gapless symmetry-protected (gSPT) phases in these setups, with particular focus on intrinsically gSPTs (igSPTs). These are symmetry protected critical points which cannot be deformed to a trivially gapped phase without spontaneously breaking the symmetry. Although these are by now well-known in (1+1)d, we demonstrate their existence in (3+1)d gauge theories. Here, they have a clear physical interpretation in terms of an obstruction to confinement, even though the full 1-form symmetry does not suffer from 't Hooft anomalies. These igSPT phases provide a new way to realize 1-form symmetries in CFTs, that has no analog for gapped phases. The SymTFT approach allows for a direct generalization from invertible symmetries to non-invertible duality symmetries, for which we study gSPT and igSPT phases as well. We accompany these theoretical results with concrete physical examples realizing such phases and explain how obstruction to confinement is detected at the level of symmetric deformations.

39 pages, 2 appendices. v2: clarified physical meaning of igSPTs for 1-form symmetries. v3: clarified several points, typos fixed, reference added

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Cited by in corpus (12)

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• Boundary SymTFT
• Symmetry Transmutation and Anomaly Matching
• Topological physics in quantum critical systems
• Projective Representations, Bogomolov Multiplier, and Their Applications in Physics
• The 3d $A$-model and generalised symmetries, Part I: bosonic Chern-Simons theories
• (2+1)d Lattice Models and Tensor Networks for Gapped Phases with Categorical Symmetry
• Spacetime symmetry-enriched SymTFT: from LSM anomalies to modulated symmetries and beyond
• Entropic order parameters and topological holography
• Analogs of deconfined quantum criticality for non-invertible symmetry breaking in 1d
• Higher-form anomalies and state-operator correspondence beyond conformal invariance
• Generalized symmetry enriched criticality in (3+1)d