We analyze the u-plane contribution to Donaldson invariants of a four-manifold X . For b2 (X) > 1, this contribution vanishes, but for b + 2 = 1, the Donaldson invariants must be written as the sum… (More)

Applications of conformal field theory to the theory of fractional quantum Hall systems are discussed. In particular, Laughlin's wave function and its cousins are interpreted as conformal blocks in… (More)

We compute the principal contribution to the index in the supersymmetric quantum mechanical systems which are obtained by reduction to 0+1 dimensions of N = 1, D = 4, 6, 10 super-Yang-Mills theories… (More)

We study relations between some topics in number theory and supersymmetric black holes. These relations are based on the “attractor mechanism” of N = 2 supergravity. In IIB string compactification… (More)

We study the effective low energy supergravity of the strongly coupled heterotic string compactified on a Calabi-Yau 3-fold with generic E8 × E8 gauge bundle. We focus on the effective potential for… (More)

This talk was divided into 3 parts. In each part we describe how considerations related to D-branes and RR fields of type II string theory naturally lead to mathematics related to K-theory. Part one… (More)

We develop some useful techinques for integrating over Higgs branches in supersymmetric theories with 4 and 8 supercharges. In particular, we define a regularized volume for hyperkahler quotients. We… (More)

We investigate a 4D analog of 2D WZW theory. The theory turns out to have surprising finiteness properties and an infinite-dimensional current algebra symmetry. Some correlation functions are… (More)

In a previous paper we showed that bracket relations uniquely fix the tree-level bosonic string S-matrix for N ≤ 26 particle scattering. In this note we extend the proof to N-1 On leave of absence… (More)