标题： 对(3+1)d无能隙SPT的SymTFT和限制禁闭的障碍 显示英文标题

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

摘要： 我们研究在存在1形式和不可逆对偶性对称性的(3+1)d中的无能隙相。 使用对称拓扑场论(SymTFT)方法，我们在这些设置中对无能隙对称保护(gSPT)相进行分类，特别关注内在的gSPT相(igSPT)。 这些是对称保护的临界点，无法在不自发破坏对称性的前提下变形为平凡的能隙相。 尽管这些在(1+1)d中现在已经广为人知，但我们展示了它们在(3+1)d规范理论中的存在。 在这里，它们在关于禁闭障碍的清晰物理解释中表现出来，尽管完整的1形式对称性没有't Hooft反常。 这些igSPT相提供了一种在共形场论(CFTs)中实现1形式对称性的新方法，这在能隙相中没有类似情况。 SymTFT方法允许从可逆对称性直接推广到不可逆对偶性对称性，我们同样研究了gSPT和igSPT相。 我们通过具体的物理实例来支持这些理论结果，并解释如何在对称性变形的层面检测禁闭障碍。 显示英文摘要

摘要： 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.