Rainbow Bridge

Rainbow Bridge (虹の橋) is a bonus side story, written by Kawahara Reki, that was included in the limited edition version of the Extra Edition volume of the DVD/BD sets for the anime. The story is a sequel to the to the Extra Edition's story.

Preview
Having finished their adventure at the Undersea Temple, Kirito and company came back to Alfheim on a whale. However, Leviathan the Sea Lord and Kraken the Abyss Lord's puzzling conversation invites them to the next adventure in line. Does the rainbow bridge, which is said to connect to the realm of the gods, Asgard, exist? The stage changes from the ocean to the skies, the new battle of the fairy swordsmen begins!