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 $E_{\gamma }\lesssim 100\mathrm{MeV}$ 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 $R\lesssim 0.9\times {10}^{-4\mathrm{}}\mathrm{mm}$; for three extra dimensions it is $R\lesssim 1.9\times {10}^{-7\mathrm{}}\mathrm{mm}$.