New supernova limit on large extra dimensions: bounds on Kaluza-Klein graviton production

If large extra dimensions exist in nature, supernova (SN) cores will emit large fluxes of Kaluza-Klein gravitons, producing a cosmic background of these particles with energies and masses up to about 100 MeV. Radiative decays then give rise to a diffuse cosmic gamma-ray background with E(gamma) approximately less than 100 MeV which is well in excess of the observations if more than 0.5%-1% of the SN energy is emitted into the new channel. For two extra dimensions we derive a conservative bound on their radius of R approximately less than 0.9 x 10(-4) mm; for three extra dimensions it is R approximately less than 1.9 x 10(-7) mm.