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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Symmetries and Strings in Field Theory and Gravity
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abstract
We discuss aspects of global and gauged symmetries in quantum field theory and quantum gravity, focusing on discrete gauge symmetries. An effective Lagrangian description of $\Z_p$ gauge theories shows that they are associated with an emergent $\Z_p$ one-form (Kalb-Ramond) gauge symmetry. This understanding leads us to uncover new observables and new phenomena in nonlinear $\sigma$-models. It also allows us to expand on Polchinski's classification of cosmic strings. We argue that in models of quantum gravity, there are no global symmetries, all continuous gauge symmetries are compact, and all charges allowed by Dirac quantization are present in the spectrum. These conjectures are not new, but we present them from a streamlined and unified perspective. Finally, our discussion about string charges and symmetries leads to a more physical and more complete understanding of recently found consistency conditions of supergravity.
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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.
A mixed F- and D-term uplift in supergravity evades the Planckian lower bound on the R-axion decay constant, allowing it to be the QCD axion and dark matter.
An SU(12)-based model unifies quark color-flavor and lepton flavor, generates Yukawas via instantons, solves strong CP with massless quarks, implements a flavored seesaw, and stabilizes the proton via a discrete gauge symmetry X = B - 3(L_i + L_j - L_k).
Eleven new anomaly-free 6D (1,0) supergravities with G_non-Abelian × U(1)_R are found that satisfy Green-Schwarz factorization and global consistency conditions, together with proofs of n_V ≡ 8 mod 12 necessity for rank-two unimodular embeddability (absent SU(2), SU(3), G2).
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
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.
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
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.
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
Color confinement arises from the lack of a global color QRF supporting isolated non-singlet relational observables, with consistency checks in lower-dimensional models.
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
Partial compositeness with inverse seesaw yields neutrino dipole moments of 10^{-6} to 10^{-8} GeV^{-1} and predicts single- and multi-photon radiative signals at MiniBooNE and MINERvA.
The paper defines cones C_BPS-B and C_BPS-BB for BPS branes in supergravity and conjectures that states in C_BPS-BB are realized as BPS states with C_BPS-B as their electric-magnetic dual when moduli-independent.
Using weight polytopes of irreducible representations, a finite list of symmetric moduli spaces satisfies the SDC decay rates; most embed from an E8(8) EFT but three cannot be obtained from string or M-theory compactifications.
Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.
Under a duality symmetry assumption, minimal supergravity coupled to two vector multiplets in D=8 is uniquely fixed in the BPS sector by anomaly cancellation, uplifts, and gauge enhancement.
Defects for discrete symmetries encoded in bordism groups Ω^ξ_2(BG) and H_2(BG;Z) are described as brane networks rather than isolated objects, extending the Cobordism Conjecture and demonstrated in 4d supergravity from string/M-theory.
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
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.
Symmetry plus perturbative gravitational scattering consistency requires the abelian charge lattice to be completely populated by single-particle states for SU(N) with N≥3 and SO(N) with N≥5.
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
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.
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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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An Intermediate Scale R-axion \& the QCD Axion
A mixed F- and D-term uplift in supergravity evades the Planckian lower bound on the R-axion decay constant, allowing it to be the QCD axion and dark matter.
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Quark-Lepton Color-Flavor Unification
An SU(12)-based model unifies quark color-flavor and lepton flavor, generates Yukawas via instantons, solves strong CP with massless quarks, implements a flavored seesaw, and stabilizes the proton via a discrete gauge symmetry X = B - 3(L_i + L_j - L_k).
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Anomaly-Free Spectra, Unimodular Lattices and 6D R-Symmetry Gauged Supergravity
Eleven new anomaly-free 6D (1,0) supergravities with G_non-Abelian × U(1)_R are found that satisfy Green-Schwarz factorization and global consistency conditions, together with proofs of n_V ≡ 8 mod 12 necessity for rank-two unimodular embeddability (absent SU(2), SU(3), G2).
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All $2D$ generalised dilaton theories from $d\geq 4$ gravities
All integrable 2D Horndeski theories (and thus many regular black-hole metrics) arise as spherical reductions of pure d≥4 gravities, which the paper terms quasi-topological.
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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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Sharpened Dynamical Cobordism
Sharpened Dynamical Cobordism ties the allowed range of critical exponent δ to theory structure ξ, flagging obstructions from non-trivial cobordism charges that require new degrees of freedom.
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Positivity of the gravitational path integral implies the axionic weak gravity conjecture
Positivity of gravitational path integral inner products requires non-perturbative instabilities in axion wormholes that break shift symmetry, implying a sharp axion weak gravity conjecture with precise constants.
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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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Wormholes as red herrings: reflection positivity and the reconstruction of unitary quantum field theories
Unitary QFTs are determined up to unitary isomorphism by closed-manifold partition functions; every reflection-positive partition function comes from a unitary QFT, so spatial wormholes do not break Hilbert-space factorization once the full charged spectrum is included.
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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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Non-invertible symmetries in the axiverse, and the imaginary wormholes
Imaginary wormholes and the IDB imply that towers of BPS EFT instantons generate infinitely many superpotential terms that break non-invertible axion shift symmetries in N=1 axiverse models.
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Neutrino Dipole Moments and Radiative Signatures from Partial Compositeness
Partial compositeness with inverse seesaw yields neutrino dipole moments of 10^{-6} to 10^{-8} GeV^{-1} and predicts single- and multi-photon radiative signals at MiniBooNE and MINERvA.
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On BPS Branes
The paper defines cones C_BPS-B and C_BPS-BB for BPS branes in supergravity and conjectures that states in C_BPS-BB are realized as BPS states with C_BPS-B as their electric-magnetic dual when moduli-independent.
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EFTs with Symmetric Moduli Spaces: the Landscape and the Swampland
Using weight polytopes of irreducible representations, a finite list of symmetric moduli spaces satisfies the SDC decay rates; most embed from an E8(8) EFT but three cannot be obtained from string or M-theory compactifications.
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The Equivalence Principle at High Energies Completes the Spectrum
Tree-level gravitational scattering under the equivalence principle mandates single-particle states in all irreducible representations constructible from a single seed charge, with equal interaction strengths.
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Uniqueness of D=8 minimal supergravity with two vector multiplets
Under a duality symmetry assumption, minimal supergravity coupled to two vector multiplets in D=8 is uniquely fixed in the BPS sector by anomaly cancellation, uplifts, and gauge enhancement.
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A missing link: Brane networks and the Cobordism Conjecture
Defects for discrete symmetries encoded in bordism groups Ω^ξ_2(BG) and H_2(BG;Z) are described as brane networks rather than isolated objects, extending the Cobordism Conjecture and demonstrated in 4d supergravity from string/M-theory.
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Bordisms between 9d type IIB supergravities and commutator widths of duality groups
Proposes a refinement of the Swampland Cobordism Conjecture for duality groups, arguing that diverging commutator widths necessitate infinitely many duality defects to realize monodromies in 9d supergravity bordisms.
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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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Completeness from Gravitational Scattering
Symmetry plus perturbative gravitational scattering consistency requires the abelian charge lattice to be completely populated by single-particle states for SU(N) with N≥3 and SO(N) with N≥5.
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Towards theory constraints on ultralight dark matter from quantum gravity
In asymptotically safe gravity, dimension-five couplings of ultralight scalar dark matter to gauge field strengths vanish and are not generated perturbatively.
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Morse-Bott inequalities, Topology Change and Cobordisms to Nothing
Morse-Bott inequalities yield homology bounds and topology-change counts for generic cobordisms to nothing in string theory compactifications.
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Accidental Peccei-Quinn Symmetry from Chiral Gauge Symmetry and Mirror QCD
A chiral U(1) gauge symmetry generates an accidental Peccei-Quinn symmetry broken by mirror QCD, solving the strong CP problem without a light axion while supplying WIMP dark matter, stochastic gravitational waves, and LHC-testable colored pNGBs.
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Sampling the Graviton Pole and Deprojecting the Swampland
A sampling-based bootstrap for graviton poles in EFTs yields non-projective bounds that fix the EFT cutoff scale relative to the Planck mass, with M/M_P ≲ 7.8 in D=5.
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Non-Invertible Symmetries in Compactified Supergravities
Non-invertible symmetry defects from 11D supergravity descend to Type IIA, splitting the Bianchi sector into invertible H[3] and twisted non-invertible F[4] parts with a BF-type auxiliary sector.
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New analytic solutions of non-SUSY black branes in $10$-D heterotic supergravity and the phase transition
New exact non-SUSY black brane solutions in 10D heterotic supergravity with two gauge charges show a spontaneous symmetry breaking and dynamical instability at low temperature that predicts additional black hole solutions.
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Bounds on Discrete Gauge Symmetries in Supergravity
Upper bounds are placed on the order of enhanced discrete gauge symmetries in supersymmetric supergravity theories with 8 or more supercharges, with some bounds saturated by string theory examples.
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Discrete $p$-Form Symmetry and Higher Coulomb Phases
Field theories with ℤ_N p-form symmetry generically admit a Coulomb phase where the infrared theory is Abelian p-form electrodynamics, illustrated via continuum and lattice examples.
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Probing High-Quality Axions with Gravitational Waves
High-quality axion models with N_DW=1 and dark matter abundance requirement restrict the gauge breaking scale to 1.6e11-1e16 GeV, yielding a band of gravitational wave signals from two-step phase transitions consistent with current observations.
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Serendipitous supersymmetric solution to the strong CP problem
Anomaly-free discrete R-symmetries plus Kim-Nilles regeneration of the mu term force an accidental U(1)_PQ whose spontaneous breaking yields a SUSY DFSZ axion that solves strong CP.
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A note on conserved worldsheet supercharges in heterotic pure spinor superstring
Derives covariant superspace constraints from BRST invariance and worldsheet conservation that recover standard 10D supersymmetry in flat space and require a normalizable spinor superfield for global supersymmetry in curved superspace.
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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.
- Conserved charges and $L_\infty$ algebras
- Big Axions
- Double fibration in G-theory and the cobordism conjecture