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Cornering Relative Symmetry Theories
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abstract
The symmetry data of a $d$-dimensional quantum field theory (QFT) can often be captured in terms of a higher-dimensional symmetry topological field theory (SymTFT). In top down (i.e., stringy) realizations of this structure, the QFT in question is localized in a higher-dimensional bulk. In many cases of interest, however, the associated $(d+1)$-dimensional bulk is not fully gapped and one must instead consider a filtration of theories to reach a gapped bulk in $D = d+m$ dimensions. Overall, this leads us to a nested structure of relative symmetry theories which descend to coupled edge modes, with the original QFT degrees of freedom localized at a corner of this $D$-dimensional bulk system. We present a bottom up characterization of this structure and also show how it naturally arises in a number of string-based constructions of QFTs with both finite and continuous symmetries.
Forward citations
Cited by 9 Pith papers
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The Line, the Strip and the Duality Defect
The XY-plaquette model is claimed to possess a continuous SO(2) non-invertible duality symmetry at arbitrary coupling, realized by open condensation defects in its symmetry TFT.
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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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Notes on (-2)-form symmetries
Introduces (-2)-form symmetries that modify the SymTFT action to relate QFTs differing by anomaly data or non-invertible symmetry associators, illustrated in 2D-4D models, fusion categories, club-sandwich RG flows, an...
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SymTFT for Continuous Symmetries: Non-linear Realizations and Spontaneous Breaking
Continuous-symmetry SymTFTs are extended to non-linear coset realizations and to spontaneous breaking using boundary and corner constructions, recovering CCWZ actions and SSB Ward identities.
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SymTFT actions, Condensable algebras and Categorical anomaly resolutions
For Q8 and Rep(Q8), the paper computes condensable algebras, identifies intrinsically gapless SPT phases, and derives fusion-category short exact sequences that resolve categorical anomalies.
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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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(-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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SymTFTs for $U(1)$ symmetries from descent
Symmetry descent is extended from discrete to continuous U(1) higher-form symmetries, yielding SymTFTs that match the Antinucci-Benini and Brennan-Sun constructions.
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The Higher Structure of Symmetries of Axion-Maxwell Theory
The paper determines the fusion interfaces and F-symbols for the non-invertible electric 1-form symmetry of 4d axion-Maxwell theory.
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