On ${\alpha }^{\prime }$-effects from $D$-branes in $4d\mathcal{N}=1$

Abstract

In this work we study type IIB Calabi-Yau orientifold compactifications in the presence of space-time filling D7-branes and O7-planes. In particular, we conclude that ${\alpha }^{\prime 2}{g}_s$-corrections to their DBI actions lead to a modification of the four-dimensional $\mathcal{N}=1$ Kähler potential and coordinates. We focus on the one-modulus case of the geometric background i.e. $h^{1,1}=1$ where we find that the ${\alpha }^{\prime 2}{g}_s$-correction is of topological nature. It depends on the first Chern form of the four-cycle of the Calabi-Yau orientifold which is wrapped by the D7-branes and O7-plane. This is in agreement with our previous F-theory analysis and provides further evidence for a potential breaking of the no-scale structure at order ${\alpha }^{\prime 2}{g}_s$. Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss ${\alpha }^{\prime }$-corrections from other D$p$-branes.

38 pages