A Chern-Simons Pandemic

Abstract

In this paper we study the consistency of generalized global symmetries in theories of quantum gravity, in particular string theory. Such global symmetries arise in theories with $(p+1)$-form gauge fields, and for spacetime dimension $d\le p+3$ there are obstructions to their breaking even by quantum effects of charged objects. In 4d theories with a 2-form gauge field (or with an axion scalar), these fields endow Schwarzschild black holes with quantum hair, a global charge leading to usual trouble with remnants. We describe precise mechanisms, and examples from string compactifications and holographic pairs, in which these problems are evaded by either gauging or breaking the global symmetry, via (suitable versions of) Stuckelberg or Kaloper-Sorbo couplings. We argue that even in the absence of such couplings, the generic solution in string theory is the breaking of the global symmetries by cubic Chern-Simons terms involving different antisymmetric tensor fields. We conjecture that any theory with (standard or higher-degree antisymmetric tensor) gauge fields is in the Swampland unless its effective action includes such Chern-Simons terms. This conjecture implies that many familiar theories, like QED (even including the charged particles required by the Weak Gravity Conjecture) or $\mathcal{N}=8$ supergravity in four dimensions, are inconsistent in quantum gravity unless they are completed by these Chern-Simons terms.

60 pages, 2 figures

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• A Tower Weak Gravity Conjecture from Infrared Consistency
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• The Weak Gravity Conjecture and Emergence from an Ultraviolet Cutoff
• Modular Fluxes, Elliptic Genera, and Weak Gravity Conjectures in Four Dimensions
• A Holographic Derivation of the Weak Gravity Conjecture
• Chern-Weil Global Symmetries and How Quantum Gravity Avoids Them
• Experimental Observation of Tensor Monopoles with a Superconducting Qudit
• Revealing tensor monopoles through quantum-metric measurements
• Photon Masses in the Landscape and the Swampland
• Constraining Neutrino Masses, the Cosmological Constant and BSM Physics from the Weak Gravity Conjecture
• Weak Gravity Conjecture, Multiple Point Principle and the Standard Model Landscape
• Complexity is Simple
• de Sitter in non-supersymmetric string theories: no-go theorems and brane-worlds
• The Weak Gravity Conjecture and the Axionic Black Hole Paradox
• Discrete Symmetries, Weak Coupling Conjecture and Scale Separation in AdS Vacua
• Tensor Berry connections and their topological invariants
• Cosmic strings from pure Yang-Mills theory
• The Weak Gravity Conjecture and Axion Strings
• Non-Invertible Symmetries in Supergravity
• Are tiny gauge couplings out of the Swampland?
• Topological violation of global symmetries in quantum gravity
• Tensor Monopoles in superconducting systems
• Discrete Gauge Symmetries and the Weak Gravity Conjecture
• Higher derivative three-form gauge theories and their supersymmetric extension
• Topological couplings in higher derivative extensions of supersymmetric three-form gauge theories
• The Fate of Discrete 1-Form Symmetries in 6d
• Irrational Monodromies of Vacuum Energy
• Phases of Inflation
• Axion species scale and axion weak gravity conjecture-like bound
• Monopole Breaking of Chern-Weil Symmetries
• Hitchhiker's Guide to the Swampland: The Cosmologist's Handbook to the string-theoretical Swampland Programme