Edward Witten, the Charles Simonyi professor of Mathematical Physics at the Institute for Advanced Study at Princeton University, gave a lecture last Thursday in the Kersten Physics Teaching Center at the Physics Colloquium.
Witten’s research has pioneered advancements in string theory and quantum field theory, as well as topology and geometry. For his contributions, Witten has been awarded various honors, including the MacArthur Fellowship (1982), the Fields Medal (1990), the National Medal of Science (2003), and he was one of Time Magazine’s 100 most influential people of 2004.
Thursday’s lecture, entitled “From the Ising Model to Quantum Gravity and Beyond,” addressed duality in physics and mathematics.
At the lecture, Witten explained how in two dimensions, the Ising Model—a square-lattice mathematical model—exhibits strong-weak duality with high and low temperatures, called the Kramers-Wannier duality.
“The transformation from the lattice to the dual lattice is also fundamental in topology, where it was the original basis for Poincare duality, which is one of the most fundamental statements in geometry,” Witten said.
He then discussed other forms of duality and how they relate to quantum field theory and string theory. Due to M-Theory, we now know that the five string theories are all related by duality. If one string theory can be transformed in some way to look exactly like another, the two are said to be dual to each other.
Electric-magnetic duality is crucial in S-duality, which is the combination of two quantum field theories, string theories, or M-theory. Witten is optimistic that quantum field theories and string theories will continue to broaden our knowledge of the natural world.
“The understanding of quark confinement, the strong coupling behavior of field theory and string theory, and counting the quantum states of a black hole” are just a few of the developments the future holds, Witten said.