We derive type IIB vacua which are very promising to put string theory to experimental test. These are Calabi-Yau compactifications with a 4D fibration over a 2D base. The moduli are fixed in such a way to obtain a very anisotropic configuration where the size of the 2D base is exponentially larger than the size of the 4D fibre. These provide stringy realisations of the supersymmetric large extra dimensions scenario and extensions of the ADD scenario which are characterised by TeV-scale strings and two micron-sized extra dimensions. We also study the phenomenological properties of hidden Abelian gauge bosons which mix kinetically with the ordinary photon and get a mass via the Green-Schwarz mechanism. We show that anisotropic compactifications lead naturally to dark forces for an intermediate string scale or even to a hidden CMB for the extreme case of TeV-scale strings.
We perform a detailed analysis of the phenomenological properties of hidden Abelian gauge bosons with a kinetic mixing with the ordinary photon within type IIB flux compactifications. We study the interplay between moduli stabilisation and the Green-Schwarz mechanism that gives mass to the hidden photon paying particular attention to the role of D-terms. We present two generic classes of explicit Calabi-Yau examples with an isotropic and an anisotropic shape of the extra dimensions showing how the last case turns out to be very promising to make contact with current experiments. In fact, aniso…
In N=1 supergravity the tree-level scalar potential of the hidden sector may have a minimum with broken local supersymmetry (SUSY) as well as a supersymmetric Minkowski vacuum. These vacua can be degenerate, allowing for a consistent implementation of the multiple point principle. The first minimum where SUSY is broken can be identified with the physical phase in which we live. In the second supersymmetric phase, in flat Minkowski space, SUSY may be broken dynamically either in the observable or in the hidden sectors inducing a tiny vacuum energy density. We argue that the exact degeneracy of …
Bajc-Melfo(\textbf{BM}) two field ($S,ϕ$) superpotentials define metastable F-term supersymmetry breaking vacua suitable as hidden sectors for calculable and realistic family and Grand Unification unification models. The undetermined vev $<S_s>$ of the Polonyi field that breaks Supersymmetry can be fixed either by coupling to N=1 Supergravity or by radiative corrections. \textbf{BM} hidden sectors extend to symmetric multiplets $(S,ϕ)_{ab}$ of a gauged $O(N_g)$ family symmetry, broken at the GUT scale, so that the $O(N_g)$ charged component vevs $<\hat S_{ab}>$ are also undetermined before acc…
We study the problem of moduli stabilisation in explicit heterotic orbifold compactifications, whose spectra contain the MSSM plus some vector-like exotics that can be decoupled. Considering all the bulk moduli, we obtain the 4D low energy effective action for the compactification, which has contributions from various, computable, perturbative and non-perturbative effects. Hidden sector gaugino condensation and string worldsheet instantons result in a combination of racetrack, KKLT and cusp-form contributions to the superpotential, which lift all the bulk moduli directions. We point out the pr…
We extend the classification of the free fermionic heterotic-string vacua to models in which the SO(10) GUT symmetry at the string scale is broken to the flipped SU(5) subgroup. In our classification method, the set of basis vectors defined by the boundary conditions which are assigned to the free fermions is fixed and the enumeration of the string vacua is obtained in terms of the Generalised GSO (GGSO) projection coefficients entering the one-loop partition function. We derive algebraic expressions for the GGSO projections for all the physical states appearing in the sectors generated by the…
We construct supersymmetric Pati-Salam flux vacua in AdS from intersecting D6-branes on T^6/(Z_2 x Z_2'). The models constructed have three generations of MSSM matter plus right-handed neutrinos. Because the cycles wrapped by the D-branes are rigid there are no extra massless fields in the adjoint representation, arising as open-string moduli. However, we find that it is problematic to break the Pati-Salam gauge symmetry to the Standard Model (SM) while keeping the SM hypercharge massless.
A Novel Construction of de Sitter Vacua in Heterotic String Theory
Irving K. Barber School of Arts and Sciences, University of British Columbia Okanagan（不列颠哥伦比亚大学奥卡纳根分校阿瑟·K·巴伯艺术与科学学院）；Canadian Quantum Research Center（加拿大量子研究中心）；Department of Mathematical Sciences, Durham University（杜伦大学数学科学系）；Computational Mathematics Group, Faculty of Sciences, Hasselt University（哈瑟尔特大学理学院计算数学组）
We introduce an $N=1$ supergravity model based on the gauged shift symmetry of a single chiral multiplet, which can be identified with the string dilaton or a compactification modulus. The model allows for a tunably small and positive value of the cosmological constant. The gravitino mass parameter and the dilaton Vacuum Expectation Value are separately tunable. In a second part we analyze the quantum consistency of these models. Recent work on anomalies in supergravity theories with Fayet-Iliopoulos terms was extended, such that their results can be interpreted from a field-theoretic point of…
我说明了存在准现实的异质弦模型，其中所有的untwisted Kaehler和复杂的结构模量，以及所有的扭曲部门模量，是由广义GSO投影。我将讨论产生这种结果的模型的条件和特点。这种模型的存在为在弦论中实现额外维度提供了一个新的视角。在这种观点中，虽然几何图像提供了一个有用的方法来分类弦真空，在唯象上可行的情况下，没有额外维度的物理实现。所考虑的模型对应于Z2 X Z2 orbifolds的六维环面，加上额外的识别内部的移位和扭曲。Z2 X Z2 Orbifold的特殊性质是它可以作用于紧致化的维数作为实维数，而不是复维数。该性质使得能够在所有六个内部坐标上进行不对称投影，这使得能够投影所有未扭曲的Kaehler和复杂结构模量。
Spinor--Vector Duality (SVD) has been observed in worldsheet constructions of heterotic--string compactifications. Recently, its realisation in the effective field theory limit of string vacua in six and five dimensions has been investigated. The SVD has been used to construct a string model that allows for an extra family universal $U(1)$, with the standard $E_6$ embedding of its charges, to remain unbroken down to low scales. Anomaly cancellation of the extra $U(1)$ charges mandates the existence of additional matter states at the extra $U(1)$ breaking scale, which affects precision measurem…
The classification method of the free fermionic heterotic string vacua is extended to models where the $SO(10)$ GUT symmetry is broken directly at the string scale to the Left-Right Symmetric subgroup. Our method involves using a fixed set of basis vectors which are defined by the boundary conditions assigned to the free fermions before enumerating the string vacua by varying the Generalised GSO (GGSO) projection coefficients. It allows the derivation of algebraic expressions for the GGSO projections for each sector that generates massless states in the models. This enables a computerised anal…
Recently it was proposed that ten-dimensional tachyonic string vacua may serve as starting points for the construction of viable four dimensional phenomenological string models which are tachyon free. This is achieved by projecting out the tachyons in the four-dimensional models using projectors other than the projector which is utilised in the supersymmetric models and those of the $SO(16)\times SO(16)$ heterotic string. We continue the exploration of this class of models by developing systematic computerised tools for their classification, the analysis of their tachyonic and massless spectra…
Classification of Left-Right Symmetric (LRS) heterotic-string vacua in the free fermionic formulation, using random generation of generalised GSO (GGSO) projection coefficients, produced phenomenologically viable models with probability $4\times 10^{-11}$. Extracting substantial number of phenomenologically viable models requires modification of the classification method. This is achieved by identifying phenomenologically amenable conditions on the Generalised GSO projection coefficients that are randomly generated at the $SO(10)$ level. Around each of these fertile cores we perform a complete…
We extend the free fermionic classification methodology to the class of standard-like heterotic-string vacua, in which the $SO(10)$ GUT symmetry is broken at the string level to $SU(3)\times SU(2)\times U(1)^2$. The space of GGSO free phase configurations in this case is vastly enlarged compared to the corresponding $SO(6)\times SO(4)$ and $SU(5)\times U(1)$ vacua. Extracting substantial numbers of phenomenologically viable models therefore requires a modification of the classification methods. This is achieved by identifying conditions on the GGSO projection coefficients, which are satisfied …
The ATLAS collaboration recently recorded possible excess in the di--boson production at the di--boson invariant mass at around 2 TeV. Such an excess may be produced if there exist additional $Z^\prime$ and/or $W^\prime$ at that scale. We survey the extra $Z^\prime$s and $W^\prime$s that may arise from semi--realistic heterotic string vacua in the free fermionic formulation in seven distinct cases including: $U(1)_{Z^\prime}\in SO(10)$; family universal $U(1)_{Z^\prime}$ not in $SO(10)$; non--universal $U(1)_{Z^\prime}$; hidden sector $U(1)$ symmetries and kinetic mixing; left--right symmetric…
We find a new class of metastable de Sitter solutions in compactifications of six-dimensional supergravity motivated by type IIB or heterotic string vacua. Two Fayet-Iliopoulos terms of a local U(1) symmetry are generated by magnetic flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The interplay between the induced D-term, the moduli dependence of the effective gauge coupling, and a nonperturbative superpotential stabilizes the moduli and determines the size of the extra dimensions.
We propose that Borcherds' Fake Monster Lie algebra is a broken symmetry of heterotic string theory compactified on $T^7 \times T^2$. As evidence, we study the fully flavored counting function for BPS instantons contributing to a certain loop amplitude. The result is controlled by $Φ_{12}$, an automorphic form for $O(2, 26, \mathbb{Z})$. The degeneracies it encodes in its Fourier coefficients are graded dimensions of a second-quantized Fock space for this large symmetry algebra. This construction provides a concrete realization of Harvey and Moore's proposed relationship between Generalized Ka…
We use a new mechanism for generating a Fayet-Iliopoulos term in supergravity, which is not associated to an R symmetry, to construct a semi-realistic theory of slow-roll inflation for a theory with the same Kähler potential and superpotential as the KKLT string background (without anti-D3 branes). In our model, supersymmetry must be broken at a high scale in a hidden sector to ensure that the cutoff of the effective field theory is above the Hubble scale of inflation. The gravitino has a super-EeV mass and supersymmetry breaking is communicated to the observable sector through gravity mediati…
We revisit an orbifold matrix model obtained as a restriction of the type IIB matrix model on a Z_3-invariant sector. An investigation of its moduli space of vacua is performed and issues related to chiral gauge theory and gravity are discussed. Modifications of the orbifolded model triggered by Chern-Simons or mass deformations are also analyzed. Certain vacua of the modified models exhibit higher-dimensional behaviour with internal geometries related to fuzzy spheres.
Using the flux compactification scenario in a generic supergravity model we construct a set of conditions which are necessary to generate de-Sitter or anti de-Sitter vacua for appropriate choices of the parameters in superpotential. It is shown that a mass spectrum consistent with softly broken TeV scale supersymmetry in a minimal supersymmetric standard model at the observable sector can be obtained along with a tiny cosmological constant when the Kahler and superpotential of the hidden sector satisfy a set of general constraints. Constructing a specific model with Kahler and superpotentials …
We use methods from topological data analysis to study the topological features of certain distributions of string vacua. Topological data analysis is a multi-scale approach used to analyze the topological features of a dataset by identifying which homological characteristics persist over a long range of scales. We apply these techniques in several contexts. We analyze N=2 vacua by focusing on certain distributions of Calabi-Yau varieties and Landau-Ginzburg models. We then turn to flux compactifications and discuss how we can use topological data analysis to extract physical informations. Fin…
The transition from formulations with extra dimensions to Kaluza-Klein theories, aimed at extending the Standard Model, bears the ingredients of hidden symmetries and the Kaluza-Klein mechanism for mass generation. We explore these essential aspects in detail, and find that much can be said about them with no reference to the specific geometry of compact extra dimensions: the low-energy theory is determined, included dynamic variables and symmetries; mass terms arise; eigenfunctions that define Kaluza-Klein fields are fixed by the appropriate choice a Casimir invariant; there is a set of Kaluz…
We analyse type IIA Calabi-Yau orientifolds with backgroud fluxes, taking into account the effect of perturbative $α'$-corrections. In particular, we consider the $α'$-corrections that modify the metrics in the Kähler sector of the compactification. As it has been argued in the literature, including such $α'$-corrections allows to construct the mirror duals of type IIB Calabi-Yau flux compactifications, in which the effect of flux backreaction is under control. We compute the $α'$-corrected scalar potential generated by the presence of RR and NS fluxes, and reformulate it as a bilinear of the …
7D (non-)susy vacua & DWs from dynamical open strings
INFN, Sezione di Roma2（意大利国家核物理研究所罗马第二分部）；Galileo Galilei Institute for Theoretical Physics（伽利略·伽利莱理论物理研究所）；Universidad de Oviedo（奥维耶多大学）；Instituto Universitario de Ciencias y Tecnologías Espaciales de Asturias (ICTEA)（阿斯图里亚斯宇宙科学与技术大学研究所）
We discuss the construction of heterotic--string models that allow for the existence of an extra $Z^\prime$ at low scales. One of the main difficulties encountered is that the desired symmetries tend to be anomalous in the prevailing three generation constructions. The reason is that these models utilise the symmetry breaking pattern $E_6\rightarrow SO(10)\times U(1)_ζ$ by GGSO projections. Consequently, $U(1)_ζ$ becomes anomalous. The spinor--vector duality that was observed in the fermionic $Z_2\times Z_2$ orbifold compactifications is used to construct a phenomenological three generation Pa…
We extend the classification of free fermionic heterotic-string models to vacua in which the SO(10) GUT symmetry is broken at the string level to the Pati-Salam subgroup. Using our classification method we recently presented the first example of a quasi--realistic heterotic-string vacuum that is free of massless exotic states. Within this method we are able to derive algebraic expressions for the generalised GSO projections for all sectors that appear in the models. This facilitates the programming of the entire spectrum analysis in a computer code. The total number of vacua in the class of mo…
We consider six-dimensional supergravity with Abelian bulk flux compactified on an orbifold. The effective low-energy action can be expressed in terms of N=1 chiral moduli superfields with a gauged shift symmetry. The D-term potential contains two Fayet-Iliopoulos terms which are induced by the flux and by the Green-Schwarz term canceling the gauge anomalies, respectively. The Green-Schwarz term also leads to a correction of the gauge kinetic function which turns out to be crucial for the existence of Minkowski and de Sitter vacua. Moduli stabilization is achieved by the interplay of the D-ter…
Working within the context of the strongly coupled $E_8\times E_8$ heterotic string theory, we analyze the $B-L$ MSSM, a realistic supersymmetric extension of the Standard Model, from both a low-energy phenomenology and high-energy string perspective. From a formal point of view, we examine different constructions of string vacua, which satisfy a series of theoretical and phenomenological constraints. Such vacua configurations are anomaly-free, preserve $N = 1$ SUSY at the compactification scale and yield the correct value for the $SO(10)$ unification scale and gauge coupling in the visible pa…
Unified description of color-electric and color-magnetic strings in hybrid vacua of $\mathcal{N}=2$ supersymmetric QCD
William I. Fine Theoretical Physics Institute, University of Minnesota（明尼苏达大学威廉·I·基础理论物理研究所）；NRC “Kurchatov Institute” - PNPI（库尔恰托夫国家研究中心-库尔恰托夫物理研究所）；St. Petersburg State University（圣彼得堡国立大学）；Steklov Mathematical Institute（斯捷克洛夫数学研究所）；ITMO University（ITMO大学）；HSE University（高等经济学院）
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。
