Edward Witten - Research

Research

Witten has made numerous contributions to theoretical physics, in work that has spawned a large number of highly mathematical results. As of August, 2011, he has more than 340 publications primarily in quantum field theory and string theory and in related areas of topology and geometry. In 2004, Time magazine wrote that Witten was "generally considered the greatest theoretical physicist in the world."

One of Witten's contributions in physics is a natural solution to the so-called hierarchy problem. The Standard Model of Particle Physics predicts a particle known as Higgs Boson. Its mass however seems much lighter than the Model predicts. Witten has shown that the mechanism of broken supersymmetry offers a natural explanation to the hierarchy problem. In supersymmetry theory, the Witten Index tells whether supersymmetry is broken or not. Witten went on to make contributions in supersymmetric gauge theories. Along with Nathan Seiberg of the Institute for Advanced Study Witten developed what is now known as Seiberg–Witten theory which is related to Donaldson theory in mathematics.

As early as 1984, Witten worked on an important problem of gravitational anomaly which contributed to what is known as the first string theory revolution. With Gary Horowitz, Philip Candelas and Andy 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. In the string theory conference at University of Southern California in the mid-1990s, Witten solved an outstanding problem of how five different versions of string theory were just the same theory which are related to one another by dualities. Witten conjectured the existence of a unifying theory called M-theory whose complete structures had not been discovered yet and non-technically could be described as what could be possibly the most fundamental physical theory of the universe. Stephen Hawking, in his book The Grand Design, wrote that M-theory may be the ultimate theory of the universe.

Another of his contributions to physics was to a result of gauge gravity duality. In 1997, Juan Maldacena formulated a result establishing a relationship between gauge theories and a theory of gravity commonly known as AdS/CFT correspondence. This discovery has dominated theoretical physics for the past 15 years and Witten's work following Maldacena's insight has shed light on this relationship. His other contributions include a simplified proof of the positive energy theorem involving spinors in general relativity, his work relating supersymmetry and Morse theory, his introduction of topological quantum field theory and related work on mirror symmetry, knot theory, twistor theory and D-branes and their intersections.

Witten was awarded the Fields Medal by the International Mathematical Union in 1990, becoming the first physicist to win the prize. Sir Michael Atiyah said of Witten, "Although he is definitely a physicist, his command of mathematics is rivaled by few mathematicians... Time and again he has surprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical theorems... he has made a profound impact on contemporary mathematics. In his hands physics is once again providing a rich source of inspiration and insight in mathematics." One such example of his impact on pure mathematics is his framework for understanding the Jones polynomial using Chern–Simons theory. This had implications for low-dimensional topology and led to quantum invariants such as the Witten–Reshetikhin–Turaev invariants.