Abstract
There are strong reasons to believe that global symmetries of quantum theories cannot be exact in the presence of gravity. While this has been argued at the qualitative level, establishing a quantitative statement is more challenging. In this work we take new steps towards quantifying symmetry violation in EFTs with gravity. First, we evaluate global charge violation by microscopic black holes present in a thermal system, which represents an irreducible, universal effect at finite temperature. Second, based on general QFT considerations, we propose that local symmetry-violating processes should be faster than black hole-induced processes at any sub-Planckian temperature. Such a proposal can be seen as part of the “swampland” program to constrain EFTs emerging from quantum gravity. Considering an EFT perspective, we formulate a con- jecture which requires the existence of operators violating global symmetry and places quantitative bounds on them. We study the interplay of our conjecture with emergent symmetries in QFT. In models where gauged U(1)’s enforce accidental symmetries, we find that constraints from the Weak Gravity Conjecture can ensure that our conjecture is satisfied. We also study the consistency of the conjecture with QFT models of emergent symmetries such as extradimensional localization, the Froggatt-Nielsen mechanism, and the clockwork mechanism.
Highlights
Symmetries have long been an important conceptual tool for understanding quantum field theories (QFTs) and quantum mechanics in general
We provide some qualitative motivations for this proposal, which we will refer to as the “Swampland Symmetry Conjecture” (SSC), and check its validity in settings where approximate global symmetries emerge at low energies
How exact can a global symmetry be while remaining consistent with quantum gravity? A path to answer this fundamental question goes through the study of black holes, which in a sense are a window into Planckian physics
Summary
Symmetries have long been an important conceptual tool for understanding quantum field theories (QFTs) and quantum mechanics in general. While gauge symmetry is a necessary ingredient for defining certain Lorentz-invariant unitary QFTs, global symmetries are instead additional postulates regarding the form of a theory, which give useful constraints on the dynamics. A continuous global symmetry implies an exactly conserved current and/or an exactly massless Goldstone boson (if non-linearly realized, i.e. spontaneously broken). Even in the absence of exact global symmetries, the concept of approximate symmetries is an extremely useful tool for studying QFTs. For example, the Standard Model features approximate chiral symmetries (broken by small Yukawa couplings), which contribute to the understanding of the pion mass and suppression of flavor-changing neutral currents. Corrections to exact conservation laws are proportional to some small parameter
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