Symmetry TFTs for 3d QFTs from M-theory

We derive the Symmetry Topological Field Theories (SymTFTs) for 3d super symmetric 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 Y7, which either is the link of a conical Calabi-Yau four-fold or part of an AdS(4) x Y-7 holographic solution. In the holographic setting we first consider the 3d 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 N = 2 quiver gauge theories whose holographic duals are based on Sasaki-Einstein 7-manifolds of type Y-7 = Y-p,Y-k(CP2). 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.

Automated summary

We derive symmetry topological field theories (SymTFTs) for 3d supersymmetric quantum field theories (QFTs) constructed in M-theory. The SymTFTs encode the symmetry structures of the QFTs, including generalized global symmetries and 't Hooft anomalies. Using differential cohomology, we derive the SymTFT by reducing M-theory on a 7-manifold, either the linkage of a conical Calabi-Yau fourfold or part of an AdS(4) x Y-7 holographic solution. In the holographic setting, we derive the SymTFT for 3d N = 6 ABJ(M) theories and 3d N = 2 quiver gauge theories, which have holographic duals based on Sasaki-Einstein 7-manifolds.