Sword Art Online: Fairy Dance

Story

Kazuto Kirigaya (aka Kirito) has beaten Sword Art Online, a VRMMORPG that transformed into a literal game of death, and returned to the real world. Unfortunately, the same cannot be said for Asuna Yuuki (aka Asuna the Flash), the girl with whom Kirito fell in love in the virtual world of Aincrad but who has yet to awaken from her game-induced slumber. As his sister, Suguha, sadly looks on, Kazuto continues to visit Asuna in the hospital in the hope of finding answers. But when one day he meets a man claiming to be Asuna's fiancé, Kazuto fears that Asuna may be lost to him forever...

Synopsis via AniList (English).