Anomalies and D-branes in the Dabholkar-Park background

TL;DR

This paper investigates D-branes in the Dabholkar-Park background, using anomalies and relative KR-theory to classify stable D-branes and construct their states, providing new insights into their stability and spectrum.

Contribution

It introduces a classification of stable D-branes in the DP background via anomalies and relative KR-theory, and constructs explicit D-brane states matching this classification.

Findings

Stable D-branes classified by relative KR-theory.

D-brane states constructed matching the spectrum.

Insights into stability via boundary Majorana fermions.

Abstract

We consider D-branes in the Dabholkar-Park (DP) background, a $9$d orientifold theory obtained by gauging symmetry in the type IIB string theory compactified on a circle. Using anomalies in the world-sheet theory, we provide physical insights into the classification of stable D-branes by relative KR-theory. The nature, such as stability, of D-branes wrapping along the compactified circle can be extracted from information about $1$d Majorana fermions on the boundary of the world-sheet. These Majorana fermions need to be introduced to consistently perform the GSO projection and the orientifold. We also construct D-brane states in the DP background. The spectrum of D-branes characterized by the relative KR-theory is correctly reproduced from the D-brane states.