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 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 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 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 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…
We revisit D3-branes at toric CY$_3$ singularities with orientifolds and their description in terms of dimer models. We classify orientifold actions on the dimer through smooth involutions of the torus. In particular, we describe new orientifold projections related to maps on the dimer without fixed points, leading to Klein bottles. These new orientifolds lead to novel $\mathcal{N}=1$ SCFT's that resemble, in many aspects, non-orientifolded theories. For instance, we recover the presence of fractional branes and some of them trigger a cascading RG-flow à la Klebanov-Strassler. The remaining in…
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 analyze the problem of the hierarchy of masses and mixings in orientifold realizations of the Standard Model. We find bottom-up brane configurations that can generate such hierarchies.
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 construct a large class of SU(5) orientifold vacua with tadpole cancellation both for the standard and the flipped case. We give a general analysis of superpotential couplings up to quartic order in orientifold vacua and identify the properties of needed Yukawa couplings as well as the baryon number violating couplings. We point out that successful generation of the perturbatively forbidden Yukawa couplings entails a generically disastrous rate for proton decay from an associated quartic term in the superpotential, generated from the same instanton effects. We search for the appropriate ins…
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.
In this thesis we explore the vacua structure of type IIA orientifold (CY) compactifications with fluxes, from the 4d and the 10d point of view. We start by reviewing type IIA Calabi-Yau orientifold compactifications with fluxes. We consider RR and NSNS fluxes, and then add (non)-geometric fluxes. We recall how the potential can be written as a bilinear expression and review the main swampland conjectures involving these scenarios. Once the basics have been setted, we perform a systematic search of vacua, using directly the 4d action. We focus first on the case with RR and NSNS fluxes and then…
We present a vast landscape of O3/O7 orientifolds that descends from the famous set of complete intersection Calabi-Yau threefolds (CICY). We give distributions of topological data relevant for phenomenology such as the orientifold-odd Hodge numbers, the D3-tadpole, and multiplicities of O3 and O7-planes. Somewhat surprisingly, almost all of these orientifolds have conifold singularities whose deformation branches are projected out by the orientifolding. However, they can be resolved, so most of the orientifolds actually descend from a much larger and possibly new set of CY threefolds that can…
Multiple Realisations of N=1 Vacua in Six Dimensions
不久前，D=6中N=1真空的例子被构造为在K3曲面上紧化的IIB型弦论的定向折叠。这些模型的有趣特征之一是D5-膜的存在，表现得像小瞬子，以及额外的张量多重态的出现。从杂化弦论的观点来看，这两种现象都是非微扰现象。虽然东方褶皱模型是研究这些非微扰杂化弦现象的自然环境，但探索这种真空是如何在杂化弦论、M理论和F理论中实现的，并考虑它们之间的关系，是有趣和有益的。特别地，我们考虑了在K3 x S^1/Z_2上紧化的M-理论模型，其中在区间上存在五个膜。有一个家庭这样的模型，产生相同的光谱作为一个子家庭的orientifold模型。通过在T^2上进一步紧化到四维，我们将它们与杂化弦谱联系起来。然后，我们使用杂种优势/IIA型对偶推导出存在的Calabi-Yau 3倍，这应该产生原来的六维orientifold谱，如果我们用它们来紧致F-理论。最后，我们详细展示了如何采取这样的F-理论紧化，返回我们的IIB型orientifold模型的限制。
We study the complex deformations of orientifolds of D3-branes at toric CY singularities, using their description in terms of dimer diagrams. We describe orientifold quotients that have fixed lines or fixed points in the dimer, and characterize the possibilities to deform them in terms of the behaviour of zig-zag paths under the orientifold symmetry. The resulting models are holographic duals to warped throats with orientifold planes. Our systematic construction provides a general class of configurations which includes models recently appeared in the context of de Sitter uplift by nilpotent go…
Orientifolds, Brane Coordinates and Special Geometry
本文报道了在D3-D 7-膜和通量的存在下，K3 x T2/Z2定向褶皱上IIB型真空的规范超重力分析。我们讨论了Minkowski真空对应的超对称临界点以及相关的模的固定，发现与以前的分析一致。一个重要的作用是通过选择的辛全纯部分的特殊几何进入计算的标量势。明确给出了相关的周期矩阵N。阐明了特殊几何与膜模的Born-Infeld作用量之间的关系。
We study $4d$ $\mathcal{N}=1$ gauge theories engineered via D-branes at orientifolds of toric singularities, where gauge anomalies are cancelled without the introduction of non-compact flavor branes. Using dimer model techniques, we derive geometric criteria for establishing whether a given singularity can admit anomaly-free D-brane configurations purely based on its toric data and the type of orientifold projection. Our results therefore extend the dictionary between geometric properties of singularities and physical properties of the corresponding gauge theories.
We consider "Orientifold field theories", namely SU(N) gauge theories with Dirac fermions in the two-index representation at high temperature. When N is even these theories exhibit a spontaneously broken Z2 centre symmetry. We study aspects of the domain wall that interpolates between the two vacua of the theory. In particular we calculate its tension to two-loop order. We compare its tension to the corresponding domain wall in a SU(N) gauge theory with adjoint fermions and find an agreement at large-N, as expected from planar equivalence between the two theories. Moreover, we provide a non-pe…
Orientifolds of Gepner models without Kähler moduli
Institut de Physique Théorique, Université Paris Saclay, CEA, CNRS（理论物理研究所，巴黎萨克雷大学，法国原子能和替代能源委员会，法国国家科学研究中心）；Institute for Mathematics and Institute for Theoretical Physics Ruprecht-Karls-Universität Heidelberg（数学研究所与理论物理研究所，海德堡大学）
Comments on $SO/Sp$ Gauge Theories from Brane Configurations with an O6 Plane
我们使用M理论的方法，在存在的orientifold O 6平面，以了解某些方面的真空N=1超对称$SO(N_c)/Sp(N_c)$规范理论在四维。通过利用O6 orientifold的一些一般性质，我们重现了以前获得的一些结果与orientifold O4平面时，味群产生的世界体积动力学的D6膜。用半无限D4膜代替D6膜，得到了N=1有质量超对称规范理论真空模空间的旋转曲线的最一般形式.
Flux vacua in type IIB compactifications on orbifolds: their finiteness and minimal string coupling
Sorbonne Université（索邦大学）；CNRS（法国国家科学研究中心）；High Energy Physics Research Unit, Faculty of Science, Chulalongkorn University（朱拉隆功大学理学院高能物理研究单元）；Dipartimento di Fisica e Astronomia, Università di Bologna（博洛尼亚大学物理与天文学系）；INFN, Sezione di Bologna（意大利国家核物理研究所博洛尼区分部）
We classify discrete modular symmetries in the effective action of Type IIB string on toroidal orientifolds with three-form fluxes, emphasizing on $T^6/\mathbb{Z}_2$ and $T^6/(\mathbb{Z}_2\times \mathbb{Z}_2^\prime)$ orientifold backgrounds. On the three-form flux background, the modular group is spontaneously broken down to its congruence subgroup whose pattern is severely constrained by a quantization of fluxes and tadpole cancellation conditions. We explicitly demonstrate that the congruence subgroups appearing in the effective action arise on magnetized D-branes wrapping certain cycles of …
In this work we analyze F-theory and Type IIB orientifold compactifications to study $α'$-corrections to the four-dimensional, $\mathcal{N} = 1$ effective actions. In particular, we obtain corrections to the Kählermoduli space metric and its complex structure for generic dimension originating from eight-derivative corrections to eleven-dimensional supergravity. We propose a completion of the $G^ 2 R^3$ and $(\nabla G)^2R^2$-sector in eleven-dimensions relevant in Calabi--Yau fourfold reductions. We suggest that the three-dimensional, $\mathcal{N}=2$ Kähler coordinates may be expressed as topol…
We construct supersymmetric $\mathrm{AdS}_4$ vacua of type IIB string theory in compactifications on orientifolds of Calabi-Yau threefold hypersurfaces. We first find explicit orientifolds and quantized fluxes for which the superpotential takes the form proposed by Kachru, Kallosh, Linde, and Trivedi. Given very mild assumptions on the numerical values of the Pfaffians, these compactifications admit vacua in which all moduli are stabilized at weak string coupling. By computing high-degree Gopakumar-Vafa invariants we give strong evidence that the $α'$ expansion is likewise well-controlled. We …
We analyse type IIA Calabi-Yau orientifolds with background fluxes and D6-branes. Rewriting the F-term scalar potential as a bilinear in flux-axion polynomials yields a more efficient description of the Landscape of flux vacua, as they are invariant under the discrete shift symmetries of the 4d effective theory. In particular, expressing the extremisation conditions of the scalar potential in terms of such polynomials allows for a systematic search of vacua. We classify families of N=0 Minkowski, N=1 AdS and N=0 AdS flux vacua, extending previous findings in the literature to the Calabi-Yau co…
