  We study a four-dimensional low-energy effective field theory derived from
extra dimensional field theories with general gauge backgrounds. We find that
products among fermionic zero-modes and lightest scalar modes are expanded by
other fermionic zero-modes and lightest scalar modes. Using this aspect, we
show that higher-order couplings among the fermionic zero-modes and the
lightest scalar mode can be decomposed into three-point couplings. This
selection rule originating from a structure of the Dirac-type operators
indicates the operator product expansion the underlying conformal field theory.
