D7-Brane Motion from M-Theory Cycles and Obstructions in the Weak Coupling Limit

TL;DR

This paper explores D7-brane dynamics in F-theory, revealing explicit moduli space descriptions and uncovering physical obstructions to brane motion in weak coupling limits due to brane and orientifold plane intersections.

Contribution

It provides an explicit parameterization of D7-brane moduli space via M-theory cycle periods and identifies physical obstructions to brane motion in weak coupling regimes.

Findings

Explicit moduli space parameterization for D7-branes on K3.

Identification of obstructions from D7/O7 intersections.

D7-brane motion decouples from base geometry deformations at weak coupling.

Abstract

Motivated by the desire to do proper model building with D7-branes and fluxes, we study the motion of D7-branes on a Calabi-Yau orientifold from the perspective of F-theory. We consider this approach promising since, by working effectively with an elliptically fibred M-theory compactification, the explicit positioning of D7-branes by (M-theory) fluxes is straightforward. The locations of D7-branes are encoded in the periods of certain M-theory cycles, which allows for a very explicit understanding of the moduli space of D7-brane motion. The picture of moving D7-branes on a fixed underlying space relies on negligible backreaction, which can be ensured in Sen's weak coupling limit. However, even in this limit we find certain 'physics obstructions' which reduce the freedom of the D7-brane motion as compared to the motion of holomorphic submanifolds in the orientifold background. These obstructions originate in the intersections of D7-branes and O7-planes, where the type IIB coupling can not remain weak. We illustrate this effect for D7-brane models on CP^1 x CP^1 (the Bianchi-Sagnotti-Gimon-Polchinski model) and on CP^2. Furthermore, in the simple example of 16 D7-branes and 4 O7-planes on CP^1 (F-theory on K3), we obtain a completely explicit parameterization of the moduli space in terms of periods of integral M-theory cycles. In the weak coupling limit, D7-brane motion factorizes from the geometric deformations of the base space.