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There exist non-trivial stationary points of the Euclidean action for an axion particle minimally coupled to Einstein gravity, dubbed wormholes.
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S. W. Hawking, “ The Effective action for wormholes,
1991
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2011
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2014
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G. Dvali, S. Folkerts and A. Franca, “ How neutrino protects the axion,
2014
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M. Montero, A. M. Uranga and I. Valenzuela, “ Transplanckian axions!?,
2015
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2015
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G. F. Giudice, M. McCullough and A. Urbano, “ Hunting for Dark Particles with Gravitational Waves,
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R. S. Gupta, Z. Komargodski, G. Perez and L. Ubaldi, “ Is the Relaxion an Axion?,
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