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Symmetry TFTs for Non-Invertible Defects
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Symmetry TFTs for Non-Invertible Defects
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Given any symmetry acting on a $d$-dimensional quantum field theory, there is an associated $(d+1)$-dimensional topological field theory known as the Symmetry TFT (SymTFT). The SymTFT is useful for decoupling the universal quantities of quantum field theories, such as their generalized global symmetries and 't Hooft anomalies, from their dynamics. In this work, we explore the SymTFT for theories with Kramers-Wannier-like duality symmetry in both $(1+1)$d and $(3+1)$d quantum field theories. After constructing the SymTFT, we use it to reproduce the non-invertible fusion rules of duality defects, and along the way we generalize the concept of duality defects to \textit{higher} duality defects. We also apply the SymTFT to the problem of distinguishing intrinsically versus non-intrinsically non-invertible duality defects in $(1+1)$d.
Forward citations
Cited by 36 Pith papers
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Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata
Lattice Kramers-Wannier-Wegner duality and 1-form SPT entanglers for Z_p symmetry in 3+1d generate groups whose fusion rules are refined by Witt non-trivial quantum cellular automata; for p=2 the group is the single-q...
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New dualities in 3d TQFTs are derived via non-invertible anyon condensation, generalizing level-rank dualities and providing new presentations for parafermion theories, c=1 orbifolds, and SU(2)_N.
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Distinct finite-temperature phase diagrams of non-invertible Kennedy--Tasaki duals
In three dimensions, a cluster-model interpolation and its non-invertible Kennedy–Tasaki dual have inequivalent finite-T phase diagrams over a finite window of the interpolation, proven exactly at s=0 and mapped by QMC.
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Non-Invertible Symmetries Mixing with Witt Non-Trivial Quantum Cellular Automata
On a 3+1d cubic lattice, the duality (gauging) and 1-form-SPT-stacking operations generate local automorphisms whose fusion rules match the continuum only up to translations and non-trivial QCAs — semion, 3-fermion, a...
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Symmetry extension by condensation defects II: general dimensions and higher-groups
Gauging A×B under a cubic mixed anomaly extends C (n=1) or folds C into a higher-group (n≥2), with the new factor generated by condensation defects and detected via triple-linking.
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Chiral Tube Algebras I: Topological Defect Lines, Twisted Modules, and Finite Gauging
Chiral tube algebras unify chiral algebras and TDLs by acting on twisted defect spaces via local and non-local currents, with modules isomorphic to twisted modules of the parent algebras.
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Entanglement fingerprint of a non-invertible symmetry: exact Fibonacci cut charges on the lattice
Even-length antiferromagnetic ground state of the critical golden chain carries exact Fibonacci cut-charge weights P_tau/P_1=phi^2 and boundary entropy log g=log phi for the duality defect.
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Fracton Topological Holography
Introduces FTH as an extension of TH/SymTFT to type-I and type-II fracton orders, demonstrating boundary switches and dualities for X-cube and Haah's code via stabilizer formalism.
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Defect Conformal Manifolds along RG Domain Walls between $\mathbb Z_N$-Parafermions and Minimal Models
RG domain walls between Z_N parafermions and minimal models support a continuous defect conformal manifold generated by a spin-1 phantom current, with transmission rate vanishing at large N.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in low-dimensional holography is reinterpreted as averaging over topological boundary conditions in a fixed SymTFT slab, reproducing Poisson moments in the Marolf-Maxfield model and Zamolodchikov me...
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Half-Spacetime Gauging of 2-Group Symmetry in 3d
Constructs non-invertible duality defects in (2+1)d QFTs from half-spacetime gauging of 2-group symmetries and derives explicit fusion rules with examples in U(1)^3 gauge theories.
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Half-Spacetime Gauging of 2-Group Symmetry in 3d
Half-spacetime gauging of 2-group symmetries in (2+1)d QFTs produces non-invertible duality defects whose fusion rules are derived explicitly from parent theories with mixed anomalies.
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SymTFT in Superspace
A supersymmetric SymTFT (SuSymTFT) is constructed as a super-BF theory on (n|m)-dimensional supermanifolds and verified for compact and chiral super-bosons in two dimensions.
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Generalized Complexity Distances and Non-Invertible Symmetries
Non-invertible symmetries define quantum gates with generalized complexity distances, and simple objects in symmetry categories turn out to be computationally complex in concrete 4D and 2D QFT examples.
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Hilbert Space Fragmentation from Generalized Symmetries
Generalized symmetries generate exponentially many Krylov sectors in quantum many-body systems, showing that Hilbert space fragmentation does not by itself imply ergodicity breaking.
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Lattice chiral symmetry from bosons in 3+1d
A bosonic lattice model realizes exact chiral symmetry and its anomaly in 3+1d, with the continuum limit a compact boson theory with axion-like coupling.
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On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
A gauging method from abelian Dijkgraaf-Witten theories yields BF-type Lagrangians for non-abelian cases via local-coefficient cohomologies and homotopy analysis.
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On the SymTFTs of Finite Non-Abelian Symmetries
Constructs BF-like 3D SymTFT Lagrangians for finite non-Abelian groups presented as extensions, yielding surface-attaching non-genuine line operators and Drinfeld-center fusion rules.
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Generalized Families of QFTs
Generalized family anomalies for broken higher-group and non-invertible symmetries constrain RG flows and IR phases of QFT families, with explicit application to deformed 4d QCD.
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The Line, the Strip and the Duality Defect
Condensation defects in SymTFT descriptions of XY-plaquette and XYZ-cube models realize non-invertible self-duality symmetries at any coupling, with a continuous SO(2) version in the XY-plaquette.
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SymTFT construction of gapless exotic-foliated dual models
Develops a Mille-feuille SymTFT construction that generates foliated and exotic dual bulk theories realizing gapless boundary models with spontaneous continuous subsystem symmetry breaking, including duals of the XY p...
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Defect Charges, Gapped Boundary Conditions, and the Symmetry TFT
Defect charges under generalized symmetries correspond one-to-one with gapped boundary conditions of the Symmetry TFT Z(C) on Y = Σ_{d-p+1} × S^{p-1} via dimensional reduction.
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On Lagrangians of Non-abelian Dijkgraaf-Witten Theories
BF Lagrangians for non-abelian DW theories (e.g. dihedral groups) are obtained by gauging H^(0) symmetries of abelian DW theories, with twisted cohomologies and condensation-defect operators verified by character-tabl...
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Notes on (-2)-form symmetries
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
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Quiver Approach to Symmetry Theories
An algebraic method using the path algebra of quivers extracts symmetry anomaly data for 5D SCFTs engineered from M-theory on Calabi-Yau cones.
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From Baby Universes to Narain Moduli: Topological Boundary Averaging in SymTFTs
Ensemble averaging in holography is reframed as averaging over topological completions of a relative theory via SymTFT boundary conditions, reproducing known moments in Marolf-Maxfield and Narain models.
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Categorical Symmetries via Operator Algebras
The symmetry category of a 2D QFT with G-symmetry and anomaly k equals the twisted Hilbert space category Hilb^k(G), whose Drinfeld center is the twisted representation category of the conjugation groupoid C*-algebra,...
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Generalized Families of QFTs
Broken higher-group and non-invertible symmetries still act on the space of couplings, and their 'family anomalies' force the infrared theory to be gapless, spontaneously broken, or interrupted by a phase transition.
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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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Generalizing quantum dimensions: Symmetry-based classification of local pseudo-Hermitian systems and the corresponding domain walls
Generalized quantum dimensions from SymTFTs classify massless and massive RG flows in pseudo-Hermitian systems and relate coset constructions to domain walls.
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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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Hilbert Space and Defect Hilbert Spaces Associated with Categorical Symmetries
A quantum mechanical framework is given for Hilbert and defect spaces of line operators in BF+kCS TQFT, with line operator action realized by convolution kernels and matches to Verlinde and semiclassical Hopf-link data.
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Self-$G$-ality in 1+1 dimensions
The paper defines self-G-ality conditions for fusion category symmetries in 1+1D systems and derives LSM-type constraints on many-body ground states along with lattice model examples.
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
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ICTP Lectures on (Non-)Invertible Generalized Symmetries
Lecture notes explain non-invertible generalized symmetries in QFTs as topological defects arising from stacking with TQFTs and gauging diagonal symmetries, plus their action on charges and the SymTFT framework.
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Lectures on Generalized Symmetries
Lecture notes that systematically introduce higher-form symmetries, SymTFTs, higher-group symmetries, and related concepts in QFT using gauge theory examples.
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