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We show how the Riemann surface Σ of N = 2 Yang-Mills field theory arises in type II string compactifications on Calabi-Yau threefolds. The relevant local geometry is given by fibrations of ALE spaces. The 3-branes that give rise to BPS multiplets in the string descend to self-dual strings on the Riemann surface, with tension determined by a canonically(More)
We present a first step towards generalizing the work of Seiberg and Wit-ten on N = 2 supersymmetric Yang-Mills theory to arbitrary gauge groups. Specifically, we propose a particular sequence of hyperelliptic genus n−1 Riemann surfaces to underly the quantum moduli space of SU (n) N = 2 supersymmetric gauge theory. These curves have an obvious(More)
We give a systematic derivation of the consistency conditions which constrain open-closed disk amplitudes of topological strings. They include the A ∞ relations (which generalize as-sociativity of the boundary product of topological field theory), as well as certain homotopy versions of bulk-boundary crossing symmetry and Cardy constraint. We discuss(More)
We show that almost all string theories, including the bosonic string, the superstring and W-string theories, possess a twisted N = 2 superconformal symmetry. This enables us to establish a connection between topological gravity and the field theoretical description of matter coupled to gravity. We also show how the BRST operators of the W n-string can be(More)
We compute certain one-loop corrections to F 4 couplings of the het-erotic string compactified on T 2 , and show that they can be characterized by holomorphic prepotentials G. We then discuss how some of these couplings can be obtained in F-theory, or more precisely from 7–brane geometry in type IIB language. We in particular study theories with E 8 × E 8(More)
Using heterotic/type II string duality, we obtain exact nonperturbative results for the point particle limit (α ′ → 0) of some particular four dimensional, N = 2 supersymmetric compactifications of heterotic strings. This allows us to recover recent exact nonpertur-bative results on N = 2 gauge theory directly from tree-level type II string theory, which(More)