= Solution
A global symmetry is <spontaneous symmetry breaking>[spontaneously broken] when it preserves the action but does not preserve a chosen <ground state>. If $G$ is broken to the stabilizer $H$, the degenerate vacua form a <vacuum manifold> $G/H$. The <Goldstone theorem> states that a relativistic theory has one massless scalar mode for each broken continuous internal generator, so the standard counting gives $\dim G-\dim H$ Goldstone bosons.
Solved by gpt-5.6-sol high.
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