q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
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Coupling a QFT to a TQFT and Duality
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abstract
We consider coupling an ordinary quantum field theory with an infinite number of degrees of freedom to a topological field theory. On R^d the new theory differs from the original one by the spectrum of operators. Sometimes the local operators are the same but there are different line operators, surface operators, etc. The effects of the added topological degrees of freedom are more dramatic when we compactify R^d, and they are crucial in the context of electric-magnetic duality. We explore several examples including Dijkgraaf-Witten theories and their generalizations both in the continuum and on the lattice. When we couple them to ordinary quantum field theories the topological degrees of freedom allow us to express certain characteristic classes of gauge fields as integrals of local densities, thus simplifying the analysis of their physical consequences.
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representative citing papers
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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.
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
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-table linking.
Color confinement arises from the lack of a global color QRF supporting isolated non-singlet relational observables, with consistency checks in lower-dimensional models.
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
(-2)-form symmetries are realized as non-genuine defects in the Symmetry TFT and relate theories with different anomaly or associator data.
Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.
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.
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
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.
Analyses of specific chiral gauge theories using generalized symmetries and anomaly matching yield rich infrared effective theories, RG flows, and light spectra.
A survey of non-invertible symmetries with constructions in the Ising model and applications to neutral pion decay and other systems.
A thermodynamic treatment of charged black holes is proposed to connect swampland conjectures to the dark dimension and dark matter using dynamical cosmological constant and quasi-static scalar fields.
citing papers explorer
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Generalized Global Symmetries
q-form global symmetries generalize ordinary symmetries to higher-dimensional charged objects, leading to new rules for amplitudes, gauging, breaking, and anomaly inflow in quantum field theories.
-
Symmetry Spans and Enforced Gaplessness
Symmetry spans enforce gaplessness when a symmetry E embedded into two larger symmetries C and D has no compatible gapped phase that restricts from both.
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Non-Invertible Anyon Condensation and Level-Rank Dualities
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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Non-Invertible Duality Defects in 3+1 Dimensions
Constructs non-invertible duality defects for one-form symmetries in 3+1D by partial gauging, derives fusion rules, proves incompatibility with trivial gapped phases, and realizes explicitly in Maxwell theory and lattice models.
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Monopoles, Center Vortices, Confinement in (3+1)d, and the Lens-Space Twisted Partition Function
Proposes torus and lens-space twisted partition functions as criteria for center-vortex and monopole condensation and proves vortex condensation implies monopole condensation in gapped phases.
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Non-Abelian and Type-A Conformal Anomalies from Euler Descent
Non-Abelian conformal anomalies are classified via Stora-Zumino descent from the Euler class, placing them on equal footing with perturbative anomalies and enabling WZW terms for anomaly matching.
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Clifford Hierarchy Stabilizer Codes: Transversal Non-Clifford Gates and Magic
Extends n-dimensional topological stabilizer codes to Clifford hierarchy versions corresponding to non-Abelian gauge theories and constructs transversal gates at the (n+1)th Clifford level.
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Higher Gauging and Non-invertible Condensation Defects
Higher gauging of 1-form symmetries on surfaces in 2+1d QFT yields condensation defects whose fusion rules involve 1+1d TQFTs and realizes every 0-form symmetry in TQFTs.
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Symmetry TFTs from String Theory
Constructs Symmetry TFTs for M-theory compactifications by reducing the topological sector of 11d supergravity on the boundary of X using differential cohomology, with applications to 7d SYM and 5d SCFTs confirmed via IIB 5-brane webs.
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de Sitter Vacua & pUniverses
The charge-p Schwinger model on de Sitter space has p distinct, locally indistinguishable, de Sitter-invariant Hadamard vacuum states produced by spontaneously broken discrete Z_p symmetries.
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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-table linking.
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Understanding Color Confinement through Quantum Reference Frames and Relational Observables
Color confinement arises from the lack of a global color QRF supporting isolated non-singlet relational observables, with consistency checks in lower-dimensional models.
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Numerical Hints for Dyon Condensation at $\theta=2\pi$ via Wilson-'t Hooft Loops in $SU(2)$ Yang-Mills Theory
Lattice computation of Wilson-'t Hooft loops supplies numerical evidence for dyon condensation at theta=2pi in SU(2) Yang-Mills.
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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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String probes, simple currents, and the no global symmetries conjecture
Chiral simple current extensions on the worldsheet reproduce and generalize obstructions to gauging center one-form symmetries in 6d and 8d string compactifications while clarifying BPS particle requirements upon circle reduction.
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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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Automorphism in Gauge Theories: Higher Symmetries and Transversal Non-Clifford Logical Gates
Automorphisms of gauge groups extend to higher or non-invertible symmetries in topological gauge theories and enable transversal non-Clifford gates in 2+1d Z_N qudit Clifford stabilizer models for N greater than or equal to 3.
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Total instanton restriction via multiverse interference: Noncompact gauge theories and (-1)-form symmetries
Continuous-universe decomposition plus (-1)-form gauging eliminates every instanton in local QFTs, realized explicitly by switching 2D U(1) gauge theories to noncompact R gauge groups.
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Candidate Gaugings of Categorical Continuous Symmetry
Candidate modular invariants and gaugings for continuous G-symmetries with anomaly k are obtained from +1 eigenspaces of semiclassical modular kernels in a BF+kCS SymTFT model.
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Exact SL(2,Z)-Structure of Lattice Maxwell Theory with $\theta$-term in Modified Villain Formulation
Ultra-local lattice Maxwell theory with a theta term has exact SL(2,Z) duality after a non-local redefinition of the S-transformation, with Wilson and 't Hooft loops transforming up to a self-linking phase.
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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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Infrared spectra of some strongly--coupled chiral gauge theories
Analyses of specific chiral gauge theories using generalized symmetries and anomaly matching yield rich infrared effective theories, RG flows, and light spectra.
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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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On Thermodynamics of Charged Black Holes, Swampland, and Dark Matter
A thermodynamic treatment of charged black holes is proposed to connect swampland conjectures to the dark dimension and dark matter using dynamical cosmological constant and quasi-static scalar fields.
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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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Snowmass White Paper: Generalized Symmetries in Quantum Field Theory and Beyond
This review summarizes transformative examples of generalized symmetries in QFT and their applications to anomalies and dynamics.
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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.