A recently conjectured relashionship between UV and IR cutoffs in an
effective field theory without quantum gravity is generalized in the presence
of large extra dimensions. Estimates for the corrections to the usual
calculation of observables within quantum field theory are used to put very
stringent limits, in some cases, on the characteristic scale of the additional
compactified dimensions. Implications for the cosmological constant problem are
also discussed.Comment: 6 pages, Latex fil