Lectures on Orientifolds and Duality

TL;DR

This work presents a structured, perturbative treatment of orientifolds and their role in connecting diverse string theories through dualities. It develops the Type-IIB framework, orbifold and orientifold constructions, and K3 compactifications, then demonstrates dualities linking Type IIA on K3, heterotic on T^4, and F-theory on K3, including fiberwise arguments and orientifold limits. The notes emphasize D-branes, tadpole cancellation, and gauge-group determinations as central tools for building consistent vacua and revealing nonperturbative connections, with extensions to six-dimensional theories bearing multiple tensor multiplets. Overall, the text shows how discrete symmetries and brane configurations illuminate the web of dualities and open up new perturbative windows into nonperturbative physics.

Abstract

This is an introduction to orientifolds with emphasis on applications to duality. Based on lectures given at the 1997 Trieste Summer School on Particle Physics and Cosmology, Italy.

Figures (13)

• Figure 1: The moduli Space of Type-IIB
• Figure 2: An open string beginning on the $i$-th D-brane and ending on the $j$-th D-brane.
• Figure 3: A massless tadpole leads to a divergence in tree channel
• Figure 4: A Surface with two boundaries, one crosscap and one handle
• Figure 5: Surfaces with $\chi=0$ in the orientifold perturbation theory