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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Symmetries in quantum field theory and quantum gravity
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abstract
In this paper we use the AdS/CFT correspondence to refine and then establish a set of old conjectures about symmetries in quantum gravity. We first show that any global symmetry, discrete or continuous, in a bulk quantum gravity theory with a CFT dual would lead to an inconsistency in that CFT, and thus that there are no bulk global symmetries in AdS/CFT. We then argue that any "long-range" bulk gauge symmetry leads to a global symmetry in the boundary CFT, whose consistency requires the existence of bulk dynamical objects which transform in all finite-dimensional irreducible representations of the bulk gauge group. We mostly assume that all internal symmetry groups are compact, but we also give a general condition on CFTs, which we expect to be true quite broadly, which implies this. We extend all of these results to the case of higher-form symmetries. Finally we extend a recently proposed new motivation for the weak gravity conjecture to more general gauge groups, reproducing the "convex hull condition" of Cheung and Remmen. An essential point, which we dwell on at length, is precisely defining what we mean by gauge and global symmetries in the bulk and boundary. Quantum field theory results we meet while assembling the necessary tools include continuous global symmetries without Noether currents, new perspectives on spontaneous symmetry-breaking and 't Hooft anomalies, a new order parameter for confinement which works in the presence of fundamental quarks, a Hamiltonian lattice formulation of gauge theories with arbitrary discrete gauge groups, an extension of the Coleman-Mandula theorem to discrete symmetries, and an improved explanation of the decay $\pi^0\to\gamma \gamma$ in the standard model of particle physics. We also describe new black hole solutions of the Einstein equation in $d+1$ dimensions with horizon topology $\mathbb{T}^p\times \mathbb{S}^{d-p-1}$.
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Low-frequency scattering calculations show scalar probes through the MMP wormhole are mostly reflected or trapped at early times with late leakage to half the black-hole cross-section, while charged massless fermions transmit with unit probability via a Callan-Rubakov-like channel.
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
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.
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.
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.
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.
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.
Quantum gravity may permit contextual deviations from the Fisher metric, inducing observer-dependent modifications to the Born rule.
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.
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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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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How traversable is a traversable wormhole?
Low-frequency scattering calculations show scalar probes through the MMP wormhole are mostly reflected or trapped at early times with late leakage to half the black-hole cross-section, while charged massless fermions transmit with unit probability via a Callan-Rubakov-like channel.
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Mind the crosscap: $\tau$-scaling in non-orientable gravity and time-reversal-invariant systems
Non-orientable topological gravity produces a resummed topological expansion whose late-time behavior matches the GOE universality class of random matrix theory for time-reversal invariant chaotic systems.
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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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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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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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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
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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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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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Information Metrics and Possible Limitations of Local Information Objectivity in Quantum Gravity
Quantum gravity may permit contextual deviations from the Fisher metric, inducing observer-dependent modifications to the Born rule.
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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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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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A note on conserved worldsheet supercharges in heterotic pure spinor superstring
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What's Done Cannot Be Undone: TASI Lectures on Non-Invertible Symmetries
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