Extra dimensions, SN1987a, and nucleon-nucleon scattering data
  One of the strongest constraints on the existence of large, compact, "gravity-only" dimensions comes from SN1987a. If the rate of energy loss into these putative extra dimensions is too high, then the neutrino pulse from the supernova will differ from that actually seen. The dominant mechanism for the production of Kaluza-Klein gravitons and dilatons in the supernova is via gravistrahlung and dilastrahlung from the nucleon-nucleon system. In this paper we compute the rates for these processes in a model-independent way using low-energy theorems which relate the emissivities to the measured nucleon-nucleon cross section. This is possible because for soft gravitons and dilatons the leading contribution to the energy-loss rate is from graphs in which the gravitational radiation is produced from external nucleon legs. Previous calculations neglected these mechanisms. We re-evaluate the bounds on toroidally-compactified "gravity-only" dimensions (GODs), and find that consistency with the observed SN1987a neutrino signal requires that if there are two such dimensions then their radius must be less than 1 micron. 
Christoph Hanhart, Daniel R. Phillips, Sanjay Reddy, and Martin J.   Savage