Non-abelian magnetic black strings versus black holes

We present $d+1-$dimensional pure magnetic Yang-Mills (YM) black strings (or $1-$branes) induced by the $d-$dimensional Einstein-Yang-Mills-Dilaton black holes. Born-Infeld version of the YM field makes our starting point which goes to the standard YM field through a limiting procedure. The lifting from black holes to black strings, (with less number of fields) is by adding an extra, compact coordinate. This amounts to the change of horizon topology from $S^{d-2}$ to a product structure. Our black string in $5-$dimensions is a rather special one, with uniform Hawking temperature and non-asymptotically flat structure. As the YM charge becomes large the string gets thinner to tend into a breaking point and transform into a $4-$% dimensional black hole.