We point out that in (open) string compactifications with non-zero NS-NS B-
field we can have large Kaluza-Klein thresholds even in the small volume li
mit. In this limit the corresponding gauge theory description is in terms o
f a compactification on a non-commutative space (e.g., a torus or an orbifo
ld thereof). Based on this observation we discuss a brane world scenario of
non-commutative unification via Kaluza-Klein thresholds. In this scenario,
the unification scale can be lowered down to the TeV-ranee, yet the corres
ponding compactification radii are smaller than the string length. We discu
ss a potential application of this scenario in the context of obtaining mix
ing between different chiral generations which is not exponentially suppres
sed - as we point out, such mixing is expected to be exponentially suppress
ed in certain setups with large volume compactifications. We also point out
that T-duality is broken by certain non-perturbative twisted open string s
ectors which are supposed to give rise to chiral generations, so that in th
e case of a small volume compactification with a rational B-field we cannot
T-dualize to a large volume description. In this sense, the corresponding
field theoretic picture of unification via Kaluza-Klein thresholds in this
setup is best described in the non-commutative language. (C) 2000 Published
by Elsevier Science B.V. All rights reserved.