  KLT relations on $S_2$ factorize closed string amplitudes into product of
open string tree amplitudes. The field theory limits of KLT factorization
relations hold in minimal coupling theory of gauge field and gravity. In this
paper, we consider the field theory limits of relations on $D_2$. Though the
relations on $D_2$ and KLT factorization relations hold on worldsheets with
different topologies, we find the field theory limits of $D_2$ relations also
hold in minimal coupling theory of gauge field and gravity. We use the $D_2$
relations to give three- and four-point tree amplitudes where gluons are
minimally coupled to gravitons. We also give a discussion on general tree
amplitudes for minimal coupling of gauge field and gravity. In general, any
tree amplitude with $M$ gravitons in addition to $N$ gluons can be given by
pure-gluon tree amplitudes with $N+2M$ legs.
