Interview with Edward Witten

Conformal Anomaly of Submanifold Observables in Ads/cft Correspondence C. Robin Graham and Edward Witten

We analyze the conformal invariance of submanifold observables associated with k-branes in the AdS/CFT correspondence. For odd k, the resulting observables are conformally invariant, and for even k, they transform with a conformal anomaly that is given by a local expression which we analyze in detail for k = 2.

Geometric Langlands And The Equations Of Nahm And Bogomolny

Geometric Langlands duality relates a representation of a simple Lie group G to the cohomology of a certain moduli space associated with the dual group G. In this correspondence, a principal SL2 subgroup of G makes an unexpected appearance. Why this happens can be explained using gauge theory, as we will see in this article, with the help of the equations of Nahm and Bogomolny. (Based on a lect...

Physical Interpretation of Certain Strong Coupling Singularities

A Short History of the Interaction Between QFT and Topology

Today’s story should involve lots of people, but the stars are Sir Michael Atiyah and Edward Witten. It begins with a paper Witten wrote in 1982, called “Supersymmetry and Morse Theory” [3]. In this paper, Witten shows how to use ‘supersymmetric quantum mechanics’ to compute the de Rham cohomology of a compact manifold, M , via Morse theory. This was perhaps the first instance of using quantum ...

Sl(2, Z) Action on Three-dimensional Conformal Field Theories with Abelian Symmetry

On the space of three-dimensional conformal field theories with U(1) symmetry and a chosen coupling to a background gauge field, there is a natural action of the group SL(2,Z). The generator S of SL(2,Z) acts by letting the background gauge field become dynamical, an operation considered recently by Kapustin and Strassler in explaining three-dimensional mirror symmetry. The other generator T ac...