Why are Calabi-Yau moduli interpreted as effective field theory fields?

[TFT]

People usually interpret the geometric modulus of a Calabi-Yau internal space as fields in the effective field theory, after compactification of a string theory on some Calabi-Yau space, without a good explanation of this interpretation. If you have a good explanation, please share with us.

 

[suprised]

People usually interpret the geometric modulus of a Calabi-Yau internal space as fields in the effective field theory, after compactification of a string theory on some Calabi-Yau space, without a good explanation of this interpretation. If you have a good explanation, please share with us.

This fact is not just a matter of interpretation, but of concrete formulas, and is explained in detail in any textbook, see eg Green-Schwarz-Witten. It just boils down to write down the vertex operators for massless fields in terms of harmonic forms on the CY.