Question
what can i use to repair the branch that split on a dwarf Japanese maple

Answer
It will all depend on where the slit is located, the size of the limb and if it is the main stem or not. On small limbs it may not be worth doing anything since over time the tree will put out new limbs. In this case just cut the broken part off. On larger limbs or the main trunk you could try putting grafting wax on the split and wrapping the wound similar to what might be done for a cut on your arm or finger. There is also a Parafilm Grafting film that can be used instead of the wax and wrap. This method could be tried with the small limb but it may not be large enough to support the weight of the warp. Tree wrap and grafting wax can be found at your local tree nursery. If the branch is split away from the main trunk there is not much that can be done except cut it off.
Here is a web link to the parafilm.
http://www.2spi.com/catalog/supp/supp4b.shtml