Context : Star formation efficiency ( SFE ) theories are currently based on statistical distributions of turbulent cloud structures and a simple model of star formation from cores .
They remain poorly tested , especially at the highest densities .

Aims : We investigate the effects of gas density on the SFE through measurements of the core formation efficiency ( CFE ) .
With a total mass of \sim 2 \times 10 ^ { 4 } ~ { } \mbox { $M _ { \odot } $ } , the W43-MM1 ridge is one of the most convincing candidate precursor of Galactic starburst clusters and thus one of the best places to investigate star formation .

Methods : We used high-angular resolution maps obtained at 3 mm and 1 mm within the W43-MM1 ridge with the IRAM Plateau de Bure Interferometer to reveal a cluster of 11 massive dense cores ( MDCs ) , and , one of the most massive protostellar cores known .
An Herschel column density image provided the mass distribution of the cloud gas .
We then measured the ‘ instantaneous ’ CFE and estimated the SFE and the star formation rate ( SFR ) within subregions of the W43-MM1 ridge .

Results : The high SFE found in the ridge ( \sim 6 % enclosed in \sim 8 pc ^ { 3 } ) confirms its ability to form a starburst cluster .
There is however a clear lack of dense cores in the northern part of the ridge , which may be currently assembling .
The CFE and the SFE are observed to increase with volume gas density while the SFR per free fall time steeply decreases with the virial parameter , \alpha _ { vir } .
Statistical models of the SFR may well describe the outskirts of the W43-MM1 ridge but struggle to reproduce its inner part , which corresponds to measurements at low \alpha _ { vir } .
It may be that ridges do not follow the log-normal density distribution , Larson relations , and stationary conditions forced in the statistical SFR models .

Conclusions :