Two families of models compete to explain the formation of high-mass stars. The quasi-static models predict the existence of high-mass pre-stellar cores sustained by a high degree of turbulence while competitive accretion models predict that high-mass proto-stellar cores evolve from low/intermediate mass proto-stellar cores in dynamic environments. We present ALMA (1.4 mm continuum emission and $^{12}$CO emission line) and MOPRA (HCO$^{+}$, H$^{13}$CO$^{+}$ and N$_2$H$^+$ molecular line emissions) observations of a sample of 9 starless massive dense cores (MDCs) discovered in a recent Herschel/HOBYS study that have masses and sizes ($sim$110 M$_odot$ and $rsim$0.1 pc, respectively) similar to the initial conditions used in the quasi-static models. The MOPRA molecular line features show that 3 of the starless MDCs are subvirialized with $alpha_{rm vir}sim$0.35, and 4 MDCs show sign of collapse. Our ALMA observations, on the other hand, show very little fragmentation within the MDCs whereas the observations resolve the Jeans length ($lambda_{rm Jeans}sim$0.03 pc) and are sensitive to the Jeans mass (M$_{rm Jeans}sim$0.65 M$_odot$) in the 9 starless MDCs. Only two of the starless MDCs host compact continuum sources, whose fluxes correspond to $<3$ M$_odot$ fragments. Therefore the mass reservoir of the MDCs has not yet been accreted onto compact objects, and most of the emission is filtered out by the interferometer. These observations do not support the quasi-static models for high-mass star formation since no high-mass pre-stellar core is found in NGC6334. The competitive accretion models, on the other hand, predict a level of fragmentation much higher than what we observe.
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