Witten's new geometry is a theoretical framework for studying the properties of space and time, called "twistor space," which he introduced in 2003.
Witten's new geometry incorporates elements from both traditional geometry and quantum mechanics, allowing for the study of curved spaces and their interactions with particles and fields.
Witten's new geometry has the potential to shed light on many open questions in physics, such as the unification of gravity and quantum mechanics, as well as applications in cosmology and particle physics.
Yes, Witten has published several papers on his new geometry, including "Perturbative gauge theory as a string theory in twistor space" and "Twistor strings and the structure of space-time."
While there is ongoing research and debate surrounding Witten's new geometry, it has garnered significant interest and attention from the scientific community and has the potential to make significant contributions to our understanding of the universe.