  The effective action describing the gapless Nambu-Goldstone, or
Anderson-Bogoliubov, mode of a zero-temperature dilute Fermi gas at unitarity
is derived up to next-to-leading order in derivatives from the microscopic
theory. Apart from a next-to-leading order term that is suppressed in the BCS
limit, the effective action obtained in the strong-coupling unitary limit is
proportional to that in the weak-coupling BCS limit.
