We study a four-dimensional low-energy effective field theory derived from extradimensional field theories with flux 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 in the underlying conformal field theory.
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