Lectures on Heterotic-Type I Duality

TL;DR

This work surveys heterotic--type I duality, detailing how six- and four-dimensional theories with extended supersymmetry relate through S-duality and M-theory/U-duality. It develops duality conjectures from effective field theories, derives one-loop and higher-derivative corrections, and performs explicit tests in Higgs and Coulomb phases of compactifications, including a concrete K3-based example and a four-dimensional STU system. The analysis shows that perturbative heterotic results map to Type I (and often Type II) descriptions in overlapping weak-coupling regimes, with world-sheet instantons translating into D-brane dynamics and higher-derivative F-terms reproducing across dual frames. The results provide concrete, calculable checks of non-perturbative duality, clarifying how moduli, prepotentials, and threshold corrections transform under the duality web, and highlighting the role of D-branes, Wilson lines, and RR couplings in realizing these equivalences.

Abstract

We present a review of heterotic-type I string duality. In particular, we discuss the effective field theory of six- and four-dimensional compactifications with N>1 supersymmetries. We then describe various duality tests by comparing gauge couplings, N=2 prepotentials, as well as higher-derivative F-terms. Based on invited lectures delivered at: 33rd Karpacz Winter School of Theoretical Physics ``Duality, Strings and Fields,'' Przesieka, Poland, 13 - 22 February 1997; Trieste Conference on Duality Symmetries in String Theory, Trieste, Italy, 1 - 4 April 1997; Cargese Summer School ``Strings, Branes and Dualities,'' Cargese, France, 26 May - 14 June 1997.