We show that the mass fraction of GMC gas (n>100 cm^-3) in dense (n>>10^4 cm^-3) star-forming clumps, observable in dense molecular tracers (L_HCN/L_CO(1-0)), is a sensitive probe of the strength and mechanism(s) of stellar feedback. Using high-resolution galaxy-scale simulations with pc-scale resolution and explicit models for feedback from radiation pressure, photoionization heating, stellar winds, and supernovae (SNe), we make predictions for the dense molecular gas tracers as a function of GMC and galaxy properties and the efficiency of stellar feedback. In models with weak/no feedback, much of the mass in GMCs collapses into dense sub-units, predicting L_HCN/L_CO(1-0) ratios order-of-magnitude larger than observed. By contrast, models with feedback properties taken directly from stellar evolution calculations predict dense gas tracers in good agreement with observations. Changing the strength or timing of SNe tends to move systems along, rather than off, the L_HCN-L_CO relation (because SNe heat lower-density material, not the high-density gas). Changing the strength of radiation pressure (which acts efficiently in the highest density gas), however, has a much stronger effect on L_HCN than on L_CO. We predict that the fraction of dense gas (L_HCN/L_CO(1-0)) increases with increasing GMC surface density; this drives a trend in L_HCN/L_CO(1-0) with SFR and luminosity which has tentatively been observed. Our results make specific predictions for enhancements in the dense gas tracers in unusually dense environments such as ULIRGs and galactic nuclei (including the galactic center).
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