Topological Open String Amplitudes On Orientifolds

TL;DR

This paper analyzes topological open string amplitudes on orientifolds without fixed planes, detailing untwisted and twisted sector contributions, BPS structures, and applications to knot invariants using topological vertex and localization methods.

Contribution

It provides a comprehensive calculation framework for open string amplitudes on orientifolds, including untwisted and twisted sectors, and links to knot theory via BPS structures.

Findings

Explicit formulas for untwisted and twisted sector contributions.

Demonstrations on toric orientifolds with D-branes.

Application to BPS structure of coloured Kauffman polynomial.

Abstract

We study topological open string amplitudes on orientifolds without fixed planes. We determine the contributions of the untwisted and twisted sectors as well as the BPS structure of the amplitudes. We illustrate our general results in various examples involving D-branes in toric orientifolds. We perform the computations by using both the topological vertex and unoriented localization. We also present an application of our results to the BPS structure of the coloured Kauffman polynomial of knots.