  In order to understand both up-type and down-type Yukawa couplings, F-theory
is a better framework than the perturbative Type IIB string theory. The duality
between the Heterotic and F-theory is a powerful tool in gaining more insights
into F-theory description of low-energy chiral multiplets. Because chiral
multiplets from bundles /\^2 V and /\^2 V^x as well as those from a bundle V
are all involved in Yukawa couplings in Heterotic compactification, we need to
translate descriptions of all those kinds of matter multiplets into F-theory
language through the duality. We find that chiral matter multiplets in F-theory
are global holomorphic sections of line bundles on what we call covering matter
curves. The covering matter curves are formulated in Heterotic theory in
association with normalization of spectral surface, while they are where
M2-branes wrapped on a vanishing two-cycle propagate in F-theory. Chirality
formulae are given purely in terms of (possibly primitive) four-form flux. In
order to complete the translation, the dictionary of the Heterotic--F theory
duality has to be refined in some aspects. A precise map of spectral surface
and complex structure moduli is obtained, and with the map, we find that
divisors specifying the line bundles correspond precisely to codimension-3
singularities in F-theory.
