Will a newborn star feel a difference between being born in Orion today, and in a massive, dusty galaxy 10 billion years ago? Forming stars at rates 100x higher than any present-day galaxy, the dust-enshrouded, sub-mm bright galaxies (SMGs) play a key role in the stellar mass assembly in the early Universe. However, our understanding of physical conditions in the star-forming regions in SMGs has been very limited, chiefly due to the coarse (> 1 kpc) resolution of mm-wave observations. Even with the full power of ALMA, multi-tracer (dust, [CII], CO) studies of the ISM in SMGs remain an extremely expensive undertaking.

I will present the recent results of molecular gas studies of probably the best-studied SMG: SDP.81 (z = 3.0), a spectacular, strongly gravitationally lensed starburst. Combining ∼40 hours of ALMA long-baseline, multi-band observations, lens modelling, and radiative transfer models, we mapped the physical conditions in this SMG at an unprecedented, ∼100 pc resolution. These results provide the first view of the physical conditions in SMGs on scales comparable to nearby galaxies and their variation on sub-kpc scales. I will also discuss the limitations of the current data, on-going VLA and ALMA studies targeting the HCN, HCO+ and radio emission in this unique source, and future survey of ISM physics of large samples of SMGs.