We present explicit examples of supergravity solutions corresponding to backreacting localised (non-intersecting) O6 planes in flux reductions of massive IIA supergravity and address some criticism towards the very existence of such solutions. We verify in detail how the smeared orientifold solution becomes a good approximation to the localised solution in the large volume/weak coupling limit, as expected. We also find an exotic solution where prior to backreaction the internal space has a boundary and when backreaction is included the boundary disappears and the space closes off. The exotic example is however outside of the supergravity approximation everywhere.
We study dimensional reductions of M-theory/type II strings down to 6D in the presence of fluxes and spacetime filling branes and orientifold planes of different types. We classify all inequivalent orientifold projections giving rise to $\mathcal{N}=(1,1)$ supergravities in 6D and work out the embedding tensor/fluxes dictionary for each of those. Finally we analyze the set of vacua for the different classes of reductions and find an abundance of "no-scale" type Minkowski vacua, as well as a few novel examples of (A)dS extrema.
The standard extremal p-brane solutions in supergravity are known to allow for a generalisation which consists of adding a linear dependence on the world-volume coordinates to the usual harmonic function. In this note we demonstrate that remarkably this generalisation goes through in exactly the same way for p-branes with fluxes added to it that correspond to fractional p-branes. We relate this to warped orientifold compactifications by trading the Dp-branes for Op-planes that solve the RR tadpole condition. This allows us to interpret the worldvolume dependence as due to lower-dimensional sca…
We investigate the effective theory of type IIA string theory on six-dimensional orientifold backgrounds with SU(2)-structure. We focus on the case of orientifolds with O6-planes, for which we compute the bosonic effective action in the supergravity approximation. For a generic SU(2)-structure background, we find that the low-energy effective theory is a gauged N=2 supergravity where moduli in both vector and hypermultiplets are charged. Since all these supergravities descend from a corresponding N=4 background, their scalar target space is always a quotient of a SU(1,1)/U(1) x SO(6,n)/SO(6)xS…
We present a concrete and consistent procedure to generate one kind of non-perturbative superpotential, including the gaugino condensation corrections and poly-instanton corrections, in type IIB orientifold compactification with four Kahler Moduli. Then we use this kind of superpotential as well as the alphaprime-corrections to Kahler potential to fix all of the four Kahler moduli on a general Calabi-Yau manifold with typical K3-fibred volume form. In our construction, the considered Calabi-Yau threefolds are K3-fibred and admit at least one del Pezzo surface and one W-surface. Searching throu…
Compactifications with D-brane and orientifold sources lead to standard gauged supergravity theories if the sources are smeared over the internal directions. It is therefore of interest to find how the solutions described by the gauged supergravity are altered by properly localising the sources. In this paper we analyse this for BPS domain wall solutions in the seven-dimensional gauged supergravity obtained from an O6 toroidal orientifold compactification in massive IIA supergravity. This is one of the simplest no-scale supergravities that can be constructed and analysed in full detail. We fin…
We study the weak gravity conjecture, the swampland distance conjecture and the emergence proposal for $\mathcal{N}=1$ orientifold compactifications of type IIB string theory with O3-/O7-planes. We allow for orientifold projections with $h^{2,1}_+\neq 0$ which gives rise to closed-string $U(1)$ gauge fields, and our findings show that certain structures present for $\mathcal N=2$ compactifications are not present for $\mathcal N=1$. In particular, assumptions about stability have to be relaxed and we encounter an ambiguity for the emergence of gauge symmetries associated with the $h^{2,1}_+$ s…
We provide the dictionary between four-dimensional gauged supergravity and type II compactifications on $\mathbb{T}^6$ with metric and gauge fluxes in the absence of supersymmetry breaking sources, such as branes and orientifold planes. Secondly, we prove that there is a unique isotropic compactification allowing for critical points. It corresponds to a type IIA background given by a product of two 3-tori with SO(3) twists and results in a unique theory (gauging) with a non-semisimple gauge algebra. Besides the known four AdS solutions surviving the orientifold projection to $\mathcal{N}=4$ in…
We describe a simple and robust mechanism that stabilizes all Kahler moduli in Type IIB orientifold compactifications. This is shown to be possible with just one non-perturbative contribution to the superpotential coming from either a D3-instanton or D7-branes wrapped on an ample divisor. This moduli-stabilization mechanism is similar to and motivated by the one used in the fluxless G_2 compactifications of M-theory. After explaining the general idea, explicit examples of Calabi-Yau orientifolds with one and three Kahler moduli are worked out. We find that the stabilized volumes of all two- an…
We review two systematic bottom-up analyses of MSSM quivers recently performed by the authors. We extend the analysis of arXiv:0905.3379 by including constraints arising from proton decay via dimension 5 operators and present all four-stack quivers in the Madrid embedding which satisfy this additional constraint. Furthermore, we investigate and make precise the interplay between mass hierarchies obtained via factorizable Yukawa textures and the presence of dimension 5 proton decay operators in MSSM orientifold compactifications. We discuss this issue in a five-stack quiver, first presented in …
The equations of motion of toroidal orientifold compactifications with fluxes are in one-to-one correspondence with gauged supergravity if the orientifold (and D-brane) sources are smeared over the compact space. This smeared limit is identical to the approximation that ignores warping. It is therefore relevant to compare quantities obtained from the gauged supergravity with the true 10d solution with localised sources. In this paper we find the correspondence between BPS domain walls in gauged SUGRA and 10D SUGRA with localised sources. Our model is the simplest orientifold with fluxes we are…
We construct global orientifold limits of singular $F$-theory vacua whose associated gauge groups are SO(3), SO(5), SO(6), $F_4$, SU(4), and Spin(7). For each limit we show a universal tadpole relation is satisfied, which is a homological identity whose dimension-zero component encodes the matching of the D3 charge between each $F$-theory compactification and its orientifold limit. While for smooth $F$-theory compactifications which admit global orientifold limits the contribution to the associated universal tadpole relation comes from its Chern class, we show that for all singular $F$-theory …
We investigate the field dependence of the gauge coupling functions of four-dimensional Type IIB orientifold and F-theory compactifications with space-time filling seven-branes. In particular, we analyze the constraints imposed by holomorphicity and covariance under shift-symmetries of the bulk and brane axions. This requires introducing quantum corrections that necessarily contain Riemann theta functions on the complex torus spanned by the D7-brane Wilson line moduli. Our findings hint towards a new underlying geometric structure for gauge coupling functions in string compactifications. We ge…
We consider type IIB flux compactifications on six-dimensional SU(2)-structure manifolds with O5- and O7-planes. These six-dimensional spaces allow not only for F_3 and H_3 fluxes but also for F_1 and F_5 fluxes. We derive the four-dimensional N=1 scalar potential for such compactifications and present one explicit example of a fully stabilized AdS vacuum with large volume and small string coupling. We then discuss cosmological aspects of these compactifications and derive several no-go theorems that forbid dS vacua and slow-roll inflation under certain conditions. We also study concrete examp…
We investigate the interplay between the string scale and phenomenological scales in orientifold compactifications. Specifically, we discuss in generality the tension that often arises in accounting for neutrino masses, Yukawa couplings, and a mu-term of the correct order and show that it often constrains the string scale M_s. The discussion focuses on two scenarios where, (1) the observed order of the neutrino masses are accounted for by a D-instanton induced "stringy" Weinberg operator, or (2) effectively via the type I seesaw mechanism with an instanton induced Majorana mass term. In both s…
We systematically investigate possibilities of realizing the spontaneous CP violation in Type IIB flux compactifications on toroidal orientifolds. Our detailed analysis leads to the presence of flat directions at degenerate CP-breaking and -conserving vacua for a generic choice of three-form fluxes, indicating that flux compactifications are not sufficient to realize the spontaneous CP violation. Furthermore, the four-dimensional CP can be embedded into the duality symmetries, namely modular symmetries for a particular choice of fluxes.
We perform a systematic analysis of globally consistent D-brane quivers which realize the MSSM, and analyze them with respect to their Yukawa couplings. Often, desired couplings are perturbatively forbidden due to the presence of global U(1) symmetries. We investigate the conditions under which D-brane instantons will induce these missing couplings without generating other phenomenological drawbacks, such as R-parity violating couplings or a mu-term which is too large. Furthermore, we systematically analyze which quivers allow for a mechanism that can account for the small neutrino masses and …
M-理论的性质K3 X我，其中我是一个线的间隔，被认为是朝着制定一个'矩阵理论'表示的情况。M-理论的这种紧化的各种限制产生了杂种优势理论和I型弦论的许多众所周知的N=1的六维紧化。这些极限之间的几何关系导致了其中一些紧化之间的弦/弦对偶。在紧化的模空间中的一个特殊点上，这激发了K 3 X I上M-理论的矩阵理论表示的部分定义，作为由N个D-膜的聚集探测的某个IA型定向折叠模型的大N极限。这样的定义在D-膜和定向折叠平面上是有启发性的，但由于超对称性的数量很少，因此必然是不完整的。它建议-以下提示orientifold模型-K3 X I紧致M-理论的完整矩阵理论表示是由大N极限的紧致化-在一个合适的“对偶”表面-的“小杂弦”N = 1六维量子理论。
Massive IIA flux compactifications and U-dualities
我们试图为hep-th/0505160中引入的弦论的大量IIA型定向折叠紧化找到一个严格的公式。一个近似的双T-对偶将这种背景转换为扭曲环面上的IIA弦论，但各种争论表明，这种几何上的东方褶皱的反作用很大。特别地，AdS计算的熵表明，在紧化的一定限度内，适合于N个M2-膜的标度，尽管不是在hep-th/0505160中研究的那个。这个特定区域的M理论升力不是四维的。我们认为背景的一般极限对应于类似于F理论的情况，其中弦耦合在紧致几何的某些区域中很小，而在其他区域中很大，因此对于这些紧致化，既不存在长波长的11 D SUGRA展开，也不存在世界片展开。最后，我们推测的性质一般紧化。
Nongeometric flux compactifications with frozen complex structure moduli have been recently studied for several phenomenological purposes. In this context, we analyze the possibility of realizing de-Sitter solutions in the context of ${\cal N} =1$ type II nongeometric flux compactifications using the ${\mathbb T}^6/({\mathbb Z}_3 \times {\mathbb Z}_3)$ toroidal orientifolds. For the type IIB case, we observe that the Bianchi identities are too strong to simultaneously allow both the NS-NS three-form flux ($H_3$) and the nongeometric ($Q$) flux to take non-zero values, which makes this model ir…
We derive the 3D N=1 superpotential for the closed string sector of type IIB supergravity on toroidal O5 orientifolds with co-calibrated G2 structure and RR background flux. We find that such compactifications can provide full closed string moduli stabilization on supersymmetric AdS$_3$ vacua, and once we include brane-supersymmetry-breaking we also find indication for the existence of classical 3D de Sitter solutions. The latter however are rather difficult to reconcile with the shape moduli stabilization and flux quantization. We also discuss the possibility of achieving scale separation in …
We investigate phenomenologically viable four- and five-stack MSSM D-brane quivers which exhibit realistic fermion mass hierarchies. In our analysis, the mass hierarchies arise either from higher order terms containing the VEV's of SM singlets or from D-instanton effects, where the latter utilizes either family splitting or a factorizable Yukawa matrix. Extending the systematic bottom-up analysis of arXiv:0905.3379, we present the only four-stack quiver with a semi-realistic Yukawa texture. Investigation of five-stack MSSM models reveals many more quivers with analogous Yukawa textures, as wel…
We investigate whether vacuum solutions in flux compactifications that are obtained with smeared sources (orientifolds or D-branes) still survive when the sources are localised. This seems to rely on whether the solutions are BPS or not. First we consider two sets of BPS solutions that both relate to the GKP solution through T-dualities: (p+1)-dimensional solutions from spacetime-filling Op-planes with a conformally Ricci-flat internal space, and p-dimensional solutions with Op-planes that wrap a 1-cycle inside an everywhere negatively curved twisted torus. The relation between the solution wi…
