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SymTFTs and Duality Defects from 6d SCFTs on 4-manifolds
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abstract
In this work we study particular TQFTs in three dimensions, known as Symmetry Topological Field Theories (or SymTFTs), to identify line defects of two-dimensional CFTs arising from the compactification of 6d $(2,0)$ SCFTs on 4-manifolds $M_4$. The mapping class group of $M_4$ and the automorphism group of the SymTFT switch between different absolute 2d theories or global variants. Using the combined symmetries, we realize the topological defects in these global variants. Our main example is $\mathbb{P}^1 \times \mathbb{P}^1$. For $N$ M5-branes the corresponding 2d theory inherits $\mathbb{Z}_N$ $0$-form symmetries from the SymTFT. We reproduce the orbifold groupoid for theories with $\mathbb{Z}_N$ $0$-form symmetries and realize the duality defects at fixed points of the coupling constant under elements of the mapping class group. We also study other Hirzebruch surfaces, del Pezzo surfaces, as well as the connected sum of $\mathbb{P}^1 \times \mathbb{P}^1$. We find a rich network of global variants connected via automorphisms and realize more interesting topological defects. Finally, we derive the SymTFT on more general 4-manifolds and provide two examples.
Forward citations
Cited by 5 Pith papers
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SymTFTs and Non-Invertible Symmetries of 6d (2,0) SCFTs of Type $D$ from M-theory
The 7d SymTFT for 6d (2,0) D_N SCFTs is derived from M-theory on AdS7 × RP4, including the outer-automorphism Z2 sector, and is used to derive non-invertible symmetries and anomaly polynomials.
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Symmetry, Symmetry Topological Field Theory and von Neumann Algebra
The symmetric-sector von Neumann algebra of a QFT violates additivity or Haag duality exactly when the Lagrangian algebra of its SymTFT contains operators beyond the identity, with a sharper criterion distinguishing t...
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SymSETs and self-dualities under gauging non-invertible symmetries
A new SymSET-based construction shows that changing symmetry fractionalization classes can change fusion rules of self-duality defects under non-invertible gauging, yielding new fusion categories such as Rep D16 and Rep SD16.
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(-1)-form symmetries from M-theory and SymTFTs
A systematic M-theory construction of SymTFTs for discrete and continuous (-1)-form symmetries, with a new 4-group structure in 4d N=1 SYM from G2 manifolds.
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SymTFT Approach to 2D Orbifold Groupoids: `t Hooft Anomalies, Gauging, and Partition Functions
The authors derive partition functions of orbifolded, fermionized, and para-fermionized 2D CFTs from topological boundary states of the 3D SymTFT, introducing para-fermionic Lagrangian algebras.
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