Symmetry TFTs for 3d QFTs from M-theory

Abstract

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory either via geometric engineering or holography. These 4d SymTFTs encode the symmetry structures of the 3d QFTs, for instance the generalized global symmetries and their 't Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold $Y_7$, which either is the link of a conical Calabi-Yau four-fold or part of an ${\text{AdS}}_4\times Y_7$ holographic solution. In the holographic setting we first consider the 3d $\mathcal{N}=6$ ABJ(M) theories and derive the BF-couplings, which allow the identification of the global form of the gauge group, as well as 1-form symmetry anomalies. Secondly, we compute the SymTFT for 3d $\mathcal{N}=2$ quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type $Y_7=Y^{p,k}(\mathbb{C}{\mathbb{P}}^2)$. The SymTFT encodes 0- and 1-form symmetries, as well as potential 't Hooft anomalies between these. Furthermore, by studying the gapped boundary conditions of the SymTFT we constrain the allowed choices for $U(1)$ Chern-Simons terms in the dual field theory.

44 pages plus appendices

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Cited by in corpus (22)

• Non-invertible Symmetries of Class $\mathcal{S}$ Theories
• Lecture Notes on Generalized Symmetries and Applications
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• Anomalies of Non-Invertible Symmetries in (3+1)d
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• Topological holography, quantum criticality, and boundary states
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• SymTFT for (3+1)d Gapless SPTs and Obstructions to Confinement
• 3d $\mathcal{N}=4$ mirror symmetry with 1-form symmetry
• Twisted Partition Functions as Order Parameters
• Trinions for the $3d$ compactification of the $5d$ rank 1 $E_{N_f+1}$ SCFTs
• Disconnected gauge groups in the infrared
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• Subsystem Symmetry-Protected Topological Phases from Subsystem SymTFT of 2-Foliated Exotic Tensor Gauge Theory
• $N$-ality symmetry and SPT phases in (1+1)d
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