Multidimensional matter is a theoretical mathematic construct which balances out certain exotic quantum gravitational models. Though no reputable scientific body has yet to have observed the existence of multidimensional matter, most scientific bodies are relatively sure that it exists in some way as a mathematical construct if not in reality.
Theory
Put simply, this type of matter exists simultaneously inside our normal space-time continuum and in adjacent subspace domains at the same time, transcending dimensional barriers. Most mathematic models suggest such matter would have unique and exotic properties impacting surrounding space-time in unpredictable ways, creating exotic subatomic particles, warping the very fabric of space-time. Some models suggest that this type of matter could be a nearly unlimited power source, while others suggest that it could provide a gateway between subspace domains. Still others suggest that nearing such matter would certainly be fatal to normal matter and that it is only created as single atoms of matter.
Rumors
Rumors in fringe science communities have long suggested that Starfleet Intelligence has found such matter and is working to weaponize it. Even rarer rumors suggest that such matter is being used to create planet sized gateways to protect the Federation from another war. Such rumors are nearly entirely seen as fringe conspiracy theories that have no scientific credibility. The most prominent scientists that once supported the idea that such matter had been found have either recanted or never seen again. A fact which is very difficult to find out.