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 α′2gs-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. h1,1 = 1 where we find that the α′2gs-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 α′2gs. Corrected background solutions for the dilaton, the warp-factor as well as the internal space metric are derived. Additionally, we briefly discuss α′-corrections from other Dp-branes.
Highlights
Background solutionWe show that the following ansatz for the type IIB background metric and dilatonΦ = φ(0) + α φ(1), φ(0) = const., ds2S = e2α A(1) ημν dxμdxν + e−2αA(1) gi(j0) + α gi(j1) dyidyj, (4.19) (4.20)is a solution to (4.13)–(4.18), where gi(j0) denotes the unmodified Calabi-Yau metric which constitutes a solution to the classical E.O.M.’s
We study Calabi-Yau orientifold compactifications with space-time filling D7-branes and O7 planes [32, 33], in particular we focus on the gravitational four-derivative α 2gs-sector of the DBI effective actions [34], respectively
While the dimensional reduction of the α 2-corrected DBI action of the D7-branes and O7-planes is performed in the one-modulus case one may use the F-theory side of the derivation to gain confidence in eq.’s (2.3) and (2.4)
Summary
We will derive the correction for the case of a Calabi-Yau orientifold with a single Kähler modulus and with eight coinciding D7’s and one O7− Note that this setup is different compared to the one studied in [27] where only a single D7-brane is present with the class of the divisor wrapped being a multiple of the one wrapped by the O7-plane, such that tadpole cancellation is guaranteed. It is worth noting that an analog correction to the Kähler coordinates appears in 3d, N = 2 originating from higher-derivative terms to eleven-dimensional supergravity i.e. the low energy limit of M-theory compactified on a Calabi-Yau fourfold [30].
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