We continue our study of heterotic/type-I duality in D<10 dimensions. We
consider the heterotic and type-I theories compactified on tori to lower
dimensions. We calculate the special (``BPS saturated'') F^4 and R^4 terms in
the effective one-loop heterotic action. These terms are expected to be
non-perturbatively exact for D>4.
The heterotic result is compared with the associated type-I result. In D<9
dimensions, the type-I theory has instanton corrections due to D1 instantons.
In D=8 we use heterotic-type I duality to give a simple prescription of the
D-instanton calculation on the type I side. We allow arbitrary Wilson lines and
show that the D1-instanton determinant is the affine character-valued elliptic
genus evaluated at the induced complex structure of the D1-brane world-volume.
The instanton result has an expansion in terms of Hecke operators that suggest
an interpretation in terms of an SO(N) matrix model of the D1-brane. The total
result can be written in terms of generalized prepotentials revealing an
underlying holomorphic structure.
In D<8 we calculate again the heterotic perturbative thresholds and show that
they agree with the D1-instanton calculation using the rules derived in D=8.Comment: Latex, 67 pages, 1 figur