Abstract
When axions are coupled to gravity, it is known that wormholes exist as gravitational instantons. These wormholes break global U(1) symmetry explicitly thus giving rise to the wormhole-induced low-energy effective Lagrangian. We derive systematically this effective Lagrangian to lower orders in the derivative expansion. The role of U(1) symmetry to the third-quantized field theory of topology change and the invisible-axion phenomenology in the wormhole background are also discussed.

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