D7-brane motion from M-theory cycles and obstructions in the weak coupling limit

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 cannot remain weak. We illustrate this effect for D7-brane models on CP 1 × 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.

Massive Abelian gauge symmetries and fluxes in F-theory

“…In this appendix we consider deforming a D n singularity to an A n−1 singularity which will allow us to identify the non-local realisation of the U(1) associated to a brane and image pair. The deformation of a D n singularity from the perspective of the cycle geometry has been discussed in great detail in [89,90]. The defining equation for a D n singularity is…”

Onα′corrections inN=1F-theory compactifications

“…When non-Abelian singularities are absent in F-theory, as in the case we consider, the corresponding Sen limit contains a single recombined D7-brane wrapping a divisor of class 8c 1 (B 3 ), as required by seven-brane tadpole cancellation. This D7-brane has the characteristic Whitney-umbrella shape [27,28].…”

Holomorphic couplings in non‐perturbative string compactifications

“…Its dual form lies then in the horizontal part H 4 H (X 4 , Z) and therefore yields the sought-after flux G 4 , see [30] for a review on such constructions. For a recent very explicit construction of these cycles in F-theory compactifications on elliptic K3 surfaces and Calabi-Yau threefolds see [271,272].…”