Traversable wormhole construction in 2+1 dimensions

We have studied traversable Lorentzian wormholes by adding some matter source involving a dilaton field into the three-dimensional low-energy string theory. Through this experiment, it was shown that there were two types of wormhole solutions---the BTZ and black string wormholes---depending on the dilaton backgrounds, respectively. We are finally able to obtain desirable solutions that confine exotic matter near the throat of a wormhole by adjusting the NS charge.