  An effective field theory of $\alpha$ cluster condensation is formulated as a
spontaneously broken symmetry in quantum field theory to understand the raison
d'etre and nature of the Hoyle and $\alpha$ cluster states in $^{12}$C. The
Nambu--Goldstone and Higgs mode operators in infinite systems are replaced with
a pair of canonical operators whose Hamiltonian gives rise to discrete energy
states in addition to the Bogoliubov--de Gennes excited states. The
calculations reproduce well the experimental spectrum of the $\alpha$ cluster
states. The existence of the Nambu--Goldstone--Higgs states is demonstrated and
crucial. The $\gamma$ decay transitions are also obtained.
