  The D theory is a $\mathcal{N}=2$ conformal SYM theory in four dimensions
with gauge group SU($N$), four matter hypermultiplets in the fundamental and
two in the anti-symmetric representation, and a flavor symmetry that contains a
U(4) factor. Its holographic dual is obtained via a combination of orbifold and
orientifold projections from Type II B string theory on $\mathrm{AdS}_5 \times
S^5$ and possesses a sector of open strings attached to D7 branes with U(4)
Chan-Paton factors. The AdS Veneziano amplitude of the U(4) gluons is dual to
four-point correlators of moment-map operators of the U(4) flavor symmetry in
the D theory. An integrated version of these correlators is captured by a
deformation of the D theory in which the fundamental hypermultiplets acquire a
mass. The partition function of this massive theory can be evaluated with
matrix-model techniques using localization. In this paper we analyze the matrix
model of the mass-deformed D theory arising from localization using the
so-called ``full Lie algebra'' approach in a $1/N$ expansion. In particular, we
study the partition function and its mass derivatives up to $O(1/N^2)$
corrections obtaining exact expressions that are valid for all values of the 't
Hooft coupling. We also analyze their behavior at strong coupling where our
results produce useful constraints on the dual open string scattering
amplitudes in AdS.
