  The 14N/15N ratio in molecules exhibits a large variation in star-forming
regions, especially when measured from N2H+ isotopologues. However, there are
only a few studies performed at high-angular resolution. We present the first
interferometric survey of the 14N/15N ratio in N2H+ obtained with the Atacama
Large Millimeter Array towards four infrared-dark clouds harbouring 3~mm
continuum cores associated with different physical properties. We detect N15NH+
(1-0) in about 20-40% of the cores, depending on the host cloud. The 14N/15N
values measured towards the millimeter continuum cores range from a minimum of
80 up to a maximum of 400. The spread of values is narrower than that found in
any previous single-dish survey of high-mass star-forming regions, and than
that obtained using the total power data only. This suggests that the 14N/15N
ratio is on average higher in the diffuse gaseous envelope of the cores, and
stresses the need for high-angular resolution maps to measure correctly the
14N/15N ratio in dense cores embedded in IRDCs. The average 14N/15N ratio of
210 is also lower than the interstellar value at the Galactocentric distance of
the clouds (300-330), although the sensitivity of our observations does not
allow us to unveil 14N/15N ratios higher than 400. No clear trend is found
between the 14N/15N ratio and the core physical properties. We find only a
tentative positive trend between 14N/15N and the H2 column density. However,
firmer conclusions can be drawn only with higher sensitivity measurements.
