On The Structure Of The Chan-Paton Factors For D-Branes In Type II Orientifolds

TL;DR

This work derives the explicit structure of Chan-Paton factors for open strings on space-filling D-branes in Type II orientifolds, establishing parity-consistency conditions that determine how O-planes of different types can coexist. It introduces a detailed o-isomorphism framework and a twist data set (B, L, α, c) that fixes the orientifold projection and the Ramond sector constraints, leading to a precise O-plane classification via the crosscap section c. The authors connect these local brane data to a global K-theory description, showing that D-brane charges in orientifolds are captured by KR^{-k}(X; c) and that twists yield twisted Real bundles, with a robust Atiyah–Singer/KR-based map between worldsheet boundary data and topological charges. They illustrate the framework with explicit circle and torus examples, relate it to non-BPS branes and ABS constructions, and develop a category-theoretic language for D-branes and their decays, providing a unified, topological view of D-brane charges in SUSY compactifications.

Abstract

We determine the structure of the Chan-Paton factors of the open strings ending on space filling D-branes in Type II orientifolds. Through the analysis, we obtain a rule concerning possible distribution of O-plane types. The result is applied to classify the topology of D-branes in terms of Fredholm operators and K-theory, deriving a proposal made earlier and extending it to more general cases. It is also applied to compactifications with N=1 supersymmetry in four-dimensions. We adapt and develop the language of category in this context, and use it to describe some decay channels.

Figures (7)

• Figure 1: State-operator correspondence
• Figure 2: Representation of an amplitude in the extended system
• Figure 3: The product ${\bf P}(\Phi)\cdot \Phi$ and its parity transform.
• Figure 4: The mode expansions
• Figure 5: T-duality between Type IIA (left) and Type IIB (right) orientifolds