Yes there is such a thing as Wudang(Wu-Tang) sword. No, the sword is not invisable, lol. It's got some similarities to taiji sword and was most likely the sword style taiji sword came from. There's no one wudang style, so there's numerous wudang sword forms out there. Here's an example of the more common modern form. While mostly based off of traditional wudang sword, I think some additional taiji & bagua was added in a couple places(frist 40-50 seconds is straight up taiji sword, and around 1:35 and a couple other places are some bagua sword techniques).