Duality and Instantons in String Theory

Abstract

In these lecture notes duality tests and instanton effects in supersymmetric vacua of string theory are discussed. A broad overview of BPS-saturated terms in the effective actions is first given. Their role in testing the consistency of duality conjectures as well as discovering the rules of instanton calculus in string theory is discussed. The example of heterotic/type-I duality is treated in detail. Thresholds of F^4 and R^4 terms are used to test the duality as well as to derive rules for calculated with D1-brane instantons. We further consider the case of R^2 couplings in N=4 ground-states. Heterotic/type II duality is invoked to predict the heterotic NS5-brane instanton corrections to the R^2 threshold. The R^4 couplings of type-II string theory with maximal supersymmetry are also analysed and the D-instanton contributions are described Other applications and open problems are sketched.

Figures (4)

• Figure 1: A type-I diagram with Euler characteristic $\chi=-1$. This contributes to the $(tr{\cal F}^2)^2$ piece of the effective action, only in degeneration limits such as the one depicted above.
• Figure 2: Embedding of the lattice $\Gamma'$ (D1-brane) in the lattice $\Gamma$ (target space torus).
• Figure 3: A D1-brane instanton correction to $tr F^4$.
• Figure 4: The three distinct ways in which the (shaded) heterotic world-sheet can wrap twice around the target-space torus.