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 AdS$_3$ and dS$_3$ vacua, but such effects seems to be hindered by the geometric flux quantization.
We evaluate string one-loop contributions to the Einstein-Hilbert term in toroidal minimally supersymmetric type IIB orientifolds with D-branes. These have potential applications to the determination of quantum corrections to the moduli Kahler metric in these models.
We use the machine learning technique to search the polytope which can result in an orientifold Calabi-Yau hypersurface and the "naive Type IIB string vacua". We show that neural networks can be trained to give a high accuracy for classifying the orientifold property and vacua based on the newly generated orientifold Calabi-Yau database with $h^{1,1}(X) \leq 6$ arXiv:2111.03078. This indicates the orientifold symmetry may already be encoded in the polytope structure. In the end, we try to use the trained neural networks model to go beyond the database and predict the orientifold signal of poly…
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 perform a Kaluza-Klein reduction of IIB supergravity including purely gravitational $α'^3$-corrections on a Calabi-Yau threefold, and perform the orientifold projection accounting for the presence of $O3/O7$-planes. We consider infinitesimal Kähler deformations of the Calabi-Yau background and derive the complete set of four-derivative couplings quadratic in these fluctuations coupled to gravity. In particular, we find four-derivative couplings of the Kähler moduli fields in the four-dimensional effective supergravity theory, which are referred to as friction couplings in the context of inf…
We revisit various aspects of AdS$_4$ flux vacua with scale separation in type II supergravity and M-theory. We show that massless IIA allows both weakly and strongly coupled solutions for which the classical orientifold backreaction can be tuned small. This is explicitly verified by computing the backreaction at leading order in perturbation theory. We give evidence that the strongly coupled solutions can be lifted to scale-separated and sourceless (but classically singular) geometries in 11D supergravity.
We study (orientifolded) toric Calabi-Yau singularities in search for D-brane configurations which lead to dynamical supersymmetry breaking at low energy. By exploiting dimer techniques we are able to determine that while most realizations lead to a Coulomb branch instability, a rather specific construction admits a fully stable supersymmetry breaking vacuum. We describe the geometric structure that a singularity should have in order to host such a construction, and present its simplest example, the Octagon.
We reconsider the two-point string scattering amplitudes of massless Neveu-Schwarz--Neveu-Schwarz states of Type IIB orientifold superstring theory on the disk and projective plane in ten dimensions and analyse its $α'$ expansion. We also discuss the unoriented Type IIB theory on $T^6/\mathbb{Z}_2\times\mathbb{Z}_2$ where two-point string scattering amplitudes of the complex Kähler moduli and complex structures of the untwisted sector are computed on the disk and projective plane. New results are obtained together with known ones. Finally, we compare string scattering amplitudes results at $α'…
Moduli Stabilization in Type IIB Orientifolds (II)
讨论了IIB型定向折叠紧化中KKLT情形下模稳定化的一般性质。特别地，我们找到了Kaehler势允许KKLT情形的条件，即h_（2，1）（X_6）=0.这样就排除了一类h_（2，1）（X_6）=0的IIB型定向褶皱。对于KKLT情形，这特别排除了所有Z_N-和Z_N x Z_M-定向折叠X_6，其中h_（2，1）（X_6）=0。这涉及Z_3，Z_7，Z_3xZ_3，Z_4xZ_4，Z_6xZ_6和Z_2xZ_6 ' -在轨道折叠点和远离轨道折叠点的情形.此外，我们还提出了一种稳定奇上同调H^（1，1）_-（X_6）的Kaehler模的机制.本文的第二部分讨论了分解的IIB型Z_N-或Z_NxZ_M - orbifold/orientifold紧化的模稳定性。作为解析的Z_6和Z_2 x Z_4轨道的例子，我们通过通量和跑道超势的组合来固定所有的模量。
We study type IIA orientifold compactifications with fluxes that give rise to perturbatively stable, non-supersymmetric AdS$_4$ vacua with D6-brane gauge sectors. Non-perturbative instabilities can be mediated by D8-branes wrapped on the six internal dimensions $X_6$, if they reduce to 4d membranes with a charge $Q$ larger than its tension $T$. The mismatch $Q \neq T$ arises due to i) curvature corrections and ii) the BIon backreaction of D6-branes wrapping 3-cycles of $X_6$. We give a simple expression for the second effect in toroidal orientifolds, and find that only pairs of 3-cycles at SU(…
We discuss flux compactifications of IIA string theory on G2 holonomy spaces with O2/O6-planes to three dimensions and find two classes of solutions: 1) No-scale Minkowski vacua from NSNS 3-form fluxes and RR 4-form fluxes. 2) By adding Romans mass we find AdS$_3$ vacua for which the AdS scale can be decoupled completely from the KK scale while the solution is at tunable weak coupling and large volume. For the AdS$_3$ vacuum we only have a proper 3D description (i.e. smeared orientifold description) of the solution like the 4D analogue of IIA moduli stabilization from fluxes and O6-planes. Thi…
We present a large class of models of D-branes at (orientifold) Calabi-Yau singularities which enjoy dynamical supersymmetry breaking at low energy, by means of either the $SU(5)$ or 3-2 supersymmetry breaking models. Once embedded in a warped throat or, equivalently, in a large $N$ theory, all models display an instability along a Coulomb branch direction towards supersymmetry preserving vacua. Interestingly, the nature of the runaway mechanism is model-independent and has a precise geometrical interpretation. This naturally suggests the properties a Calabi-Yau singularity should have in orde…
In this paper, we are looking for $\mathcal{N}=1$, AdS$_4$ sourceless vacua in type IIB. While several examples exist in type IIA , there exists only one example of such vacua in type IIB . Thanks to the framework of generalized geometry we were able to devise a semi-algorithmical method to look for sourceless vacua. We present this method, which can easily be generalized to more complex cases, and give two new vacua in type IIB.
Starting from a peculiar orientifold projection proposed long ago by Angelantonj and Cardella, we elaborate on a novel perturbative scenario that involves only D-branes, together with the two types of orientifold planes ${\rm O}_{\pm}$ and anti-orientifold planes $\overline{\rm O}_{\pm}$. We elucidate the microscopic ingredients of such models, connecting them to a novel realization of brane supersymmetry breaking. Depending on the position of the D-branes in the internal space, supersymmetry can be broken at the string scale on branes, or alternatively only at the massive level. The main nove…
We study moduli stabilization in Calabi-Yau orientifold compactifications of type IIB string theory with O3- and O7-planes. We consider a Calabi-Yau three-fold with Hodge number $h^{2,1}=50$ and stabilize all axio-dilaton and complex-structure moduli by three-form fluxes. This is a challenging task, especially for large moduli-space dimensions. To address this question we develop an algorithm to generate $10^5$ flux vacua with small flux number $N_{\rm flux}$. Based on recent results by Crinò et al. we estimate the bound imposed by the tadpole-cancellation condition as $N_{\rm flux}\leq \mathc…
In this note I demonstrate that certain findings on IIB flux compactifications in the large complex structure limit, when combined with recent statistical bounds on the large $h^{2,1}$ limit, are compatible with the Tadpole Conjecture, contrary to previous claims.
In this work we study ten-dimensional solutions to type IIA string theory of the form AdS$_4$ x $X_6$ which contain orientifold planes and preserve N=1 supersymmetry. In particular, we consider solutions which exhibit some key features of the four-dimensional DGKT proposal for compactifications on Calabi-Yau manifolds with fluxes, and in this sense may be considered their ten-dimensional uplifts. We focus on the supersymmetry equations and Bianchi identities, and find solutions to these that are valid at the two-derivative level and at first order in an expansion parameter which is related to …
We consider massive type IIA orientifold compactifications of the form AdS$_4 \times X_6$, where $X_6$ admits a Calabi-Yau metric and is threaded by background fluxes. From a 4d viewpoint, fluxes generate a potential whose vacua have been classified, including one $\mathcal{N}=1$ and three perturbatively stable $\mathcal{N}=0$ branches. We reproduce this result from a 10d viewpoint, by solving the type IIA equations at the same level of detail as previously done for the $\mathcal{N}=1$ branch. All solutions exhibit localised sources and parametric scale separation. We then analyse the non-pert…
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 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 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.
