  We present limits for the compactification scale in the theory of Large Extra
Dimensions (LED) proposed by Arkani-Hamed, Dimopoulos, and Dvali. We use 11
months of data from the Fermi Large Area Telescope (Fermi-LAT) to set gamma ray
flux limits for 6 gamma-ray faint neutron stars (NS). To set limits on LED we
use the model of Hannestad and Raffelt (HR) that calculates the Kaluza-Klein
(KK) graviton production in supernova cores and the large fraction subsequently
gravitationally bound around the resulting NS. The predicted decay of the bound
KK gravitons to {\gamma}{\gamma} should contribute to the flux from NSs.
Considering 2 to 7 extra dimensions of the same size in the context of the HR
model, we use Monte Carlo techniques to calculate the expected differential
flux of gamma-rays arising from these KK gravitons, including the effects of
the age of the NS, graviton orbit, and absorption of gamma-rays in the
magnetosphere of the NS. We compare our Monte Carlo-based differential flux to
the experimental differential flux using maximum likelihood techniques to
obtain our limits on LED. Our limits are more restrictive than past EGRET-based
optimistic limits that do not include these important corrections.
Additionally, our limits are more stringent than LHC based limits for 3 or
fewer LED, and comparable for 4 LED. We conclude that if the effective Planck
scale is around a TeV, then for 2 or 3 LED the compactification topology must
be more complicated than a torus.
