Localized modes at a D-brane--O-plane intersection and heterotic Alice strings

TL;DR

The work investigates a defect system of $N_c$ D3-branes intersecting $D7$-branes and $O7$-planes in 1+1 dimensions to understand chiral fermion zero-modes localized at the intersection. It combines anomaly inflow, index theory, and explicit zero-mode construction to show that D3-localized chiral zero-modes must exist near the $O7$-planes (especially in the compact case), with their structure consistent with an antisymmetric $O(N_c)$ representation and a realization as D1-string worldsheet degrees of freedom in the orientifold limit. The paper then maps these modes through string dualities to heterotic matrix-string theory and derives how the D1/heterotic coupling depends on the 7-brane moduli, establishing a concrete link between F-theory on K3 and heterotic moduli spaces, and argues for an $AdS_3$ dual at large $N_c$ for the heterotic matrix string CFT. Overall, the results illuminate the defect CFT structure, anomaly cancellation, and moduli-dependent couplings in this rich D-brane/O-plane system, with implications for holography and matrix-string descriptions.

Abstract

We study a system of $N_c$ $D3$-branes intersecting $D7$-branes and $O7$-planes in 1+1-dimensions. We use anomaly cancellation and string dualities to argue that there must be chiral fermion zero-modes on the $D3$-branes which are localized near the $O7$-planes. Away from the orientifold limit we verify this by using index theory as well as explicit construction of the zero-modes. This system is related to F-theory on K3 and heterotic matrix string theory, and the heterotic strings are related to Alice string defects in $\mathcal{N}=4$ Super-Yang-Mills. In the limit of large $N_c$ we find an $AdS_3$ dual of the heterotic matrix string CFT.