If I take the theory as we have it now, literally, I would conclude that extra dimensions really exist. They're part of nature. We don't really know how big they are yet, but we hope to explore that in various ways.

This had implications for low-dimensional topology and led to quantum invariants such as the Witten–ReEdward Wittentikhin–Turaev invariants. He is the son of Lorraine (Wollach) Witten and Louis Witten a theoretical physicist specializing in gravitation and general relativity. With Gary Horowitz Philip Candelas and Andrew Strominger Witten showed how string theory can lead to realistic descriptions by compactifying the theory on a higher dimensional manifold known as Calabi–Yau manifolds.

Witten is a researcher in superstring theory a theory of quantum gravity supersymmetric quantum field theories and other areas of mathematical physics. He has made contributions in mathematics and helped bridge gaps between fundamental physics and other areas of mathematics.