Non-commutative Unification in Brane World

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 limit. In this limit the corresponding gauge theory description is in terms of a compactification on a non-commutative space (e.g., a torus or an orbifold 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-range, yet the corresponding compactification radii are smaller than the string length. We discuss a potential application of this scenario in the context of obtaining mixing between different chiral generations which is not exponentially suppressed - as we point out, such mixing is expected to be exponentially suppressed in certain setups with large volume compactifications. We also point out that T-duality is broken by certain non-perturbative twisted open string sectors which are supposed to give rise to chiral generations, so that in the 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.