From diffuse extragalactic and galactic gamma rays to limits on extra
  dimensions
  We derive the maximum fraction of energy emitted in the form of massive
(Kaluza- Klein) gravitons by core collapse supernovae, and the corresponding
minimal extra-dimensional Planck mass M* in the ADD gravity framework at TeV
scales. Our constraints arise: a) from the extragalactic gamma ray background
observed by Fermi-LAT after astrophysical sources have been removed, and b) via
the residual galactic emission left after astrophysical and potentially dark
matter emission have been removed. We focus on a number of extra dimensions 3
and 4, since M* is then in the TeV range, where astrophysical and collider
constraints compete. Lower limits on M* are derived in case a) of 8.0 TeV and
1.1 TeV, and in case b) of 16 TeV and 1.9 TeV, for a number of extra dimensions
n=3 and n=4 respectively. These limits are especially robust and insensitive to
the various uncertainties involved.
