Brane Curvature Corrections to the $\mathcal{N}=1$ Type II/F-theory Effective Action

TL;DR

The paper investigates curvature-induced corrections to the 4D Kähler potential in N=1 type II/F-theory compactifications, focusing on D-brane and O-plane actions. It shows that a previously proposed α′^2 g_s correction is an artifact of a particular M-theory frame and can be removed by an 11D metric redefinition, while identifying two genuine mechanisms that can modify the volume dependence of the Kähler potential: induced Einstein-Hilbert terms on warped brane worldvolumes and induced D3-brane charge from WZ curvature couplings. The authors argue that, although these corrections can appear (e.g., at α′^2 g_s^2 for intersecting D7/O7), extended no-scale structure typically keeps their impact on the scalar potential subleading, preserving standard moduli stabilization logic. They also discuss open–closed mixing corrections arising at tree level from induced D3 charge on D7-branes and outline avenues for applying these insights to F-theory and more general setups.

Abstract

We initiate a study of corrections to the Kähler potential of $\mathcal{N}=1$ type II/F-theory compactifications that arise from curvature terms in the action of D-branes and orientifold planes. We first show that a recently proposed correction to the Kähler coordinates, which was argued to appear at order $α^{\prime 2}g_s$ and be proportional to the intersection volume of D7-branes and O7-planes, is an artifact of an inconvenient field basis in the dual M-theory frame and can be removed by a field redefinition of the 11D metric. We then analyze to what extent curvature terms in the DBI and WZ action may still lead to corrections of a similar kind and identify two general mechanisms that can potentially modify the volume dependence of the Kähler potential in the presence of D-branes and O-planes. The first mechanism is related to an induced Einstein-Hilbert term on warped brane worldvolumes, which leads to a shift in the classical volume of the compactification manifold. The resulting corrections are generic and can appear at one-loop order on branes and O-planes of various dimensions and for configurations with or without intersections. We discuss in detail the example of intersecting D7-branes/O7-planes, where a correction can appear already at order $α^{\prime 2}g_s^2$ in the Kähler potential. Due to an extended no-scale structure, however, it is then still subleading in the scalar potential. We also discuss a second mechanism, which is due to an induced D3-brane charge in the WZ action of D7-branes. Contrary to the first type of corrections, it appears at open string tree-level and shifts the definition of the Kähler coordinates in terms of the classical volume but leaves the volume itself uncorrected. Our work has implications for moduli stabilization and model building and suggests interesting generalizations to F-theory.