Analytics of type IIB flux vacua and their mass spectra

We analyze the tree-level potential of type IIB flux compactifications in warped Calabi-Yau orientifolds, in regions of weak coupling and moderately large complex structure. In this regime, one may approximate the flux-induced superpotential $W$ by a polynomial on the axio-dilaton and complex structure fields, and a significant fraction of vacua corresponds to a quadratic $W$. In this quadratic case, we argue that vacua fall into three classes, for which one can push the analytic description of their features. In particular, we provide analytic expressions for the vacuum expectation values and flux-induced masses of the axio-dilaton and complex structure fields in a large subclass of vacua, independently of the Calabi-Yau and the number of moduli. We show that supersymmetric vacua always contain flat directions, at least at this level of approximation. Our findings allow to generate vast ensembles of flux vacua in specific Calabi-Yau geometries, as we illustrate in a particular example.Comment: 36 pages + appendices, 5 figure

New families of scale separated vacua

Massive type IIA flux compactifications of the form AdS$_4 \times X_6$, where $X_6$ admits a Calabi-Yau metric and O6-planes wrapping three-cycles, display families of vacua with parametric scale separation between the compactification scale and the AdS$_4$ radius, generated by an overall rescaling of internal four-form fluxes. For toroidal orbifolds one can perform two T-dualities and map this background to an orientifold of massless type IIA compactified on an SU(3)-structure manifold with fluxes. Via a 4d EFT analysis, we generalise this last construction and embed it into new branches of supersymmetric and non-supersymmetric vacua with similar features. We apply our results to propose new infinite families of vacua based on elliptic fibrations with metric fluxes. Parametric scale separation is achieved by an asymmetric flux rescaling which, however, in general is not a simple symmetry of the 4d equations of motion. At this level of approximation the vacua are stable but, unlike in the Calabi-Yau case, they display a non-universal mass spectrum of light fields.Comment: 33 pages + appendices, 4 figure

Symmetric fluxes and small tadpoles

The analysis of type IIB flux vacua on warped Calabi--Yau orientifolds becomes considerably involved for a large number of complex structure fields. We however show that, for a quadratic flux superpotential, one can devise simplifying schemes which effectively reduce the large number of equations down to a few. This can be achieved by imposing the vanishing of certain flux quanta in the large complex structure regime, and then choosing the remaining quanta to respect the symmetries of the underlying prepotential. One can then implement an algorithm to find large families of flux vacua with a fixed flux tadpole, independently of the number of fields. We illustrate this approach in a Calabi--Yau manifold with 51 complex structure moduli, where several reduction schemes can be implemented in order to explicitly solve the vacuum equations for that sector. Our findings display a flux-tadpole-to-stabilized-moduli ratio that is marginally above the bound proposed by the Tadpole Conjecture, and we discuss several effects that would take us below such a bound.Comment: 42 pages + appendices, 3 figure

Théorie des cordes : Brisure de supersymétrie, stabilisation des modules et aspects cosmologiques

The purpose of this thesis is to explore various aspects of string theory, a unified theory of matter and all fundamental interactions including gravity. In a first chapter, we start by describing some useful key ingredients of the theory and its construction to motivate the works presented in this manuscript. We then explore three different aspects of the theory. First, a new supersymmetry-breaking mechanism in unoriented open-string models is developed. The features of this breaking are described, commented and put into perspective with other existing mechanisms. Second, one-loop masses acquired by tree-level moduli are studied in a type I string context with N=2 N=0 spontaneous breaking of supersymmetry implemented by a Scherk--Schwarz mechanism. Different strategies are followed to conclude on the stability or not at one loop of the wide variety of moduli present in the model. These strategies range from the Taylor expansion of the effective potential up to quadratic order, to the evaluation of genus-1 two-point correlation functions, through arguments arising from the duality between the heterotic and type I string. Once all the masses are computed, we give explicit models (brane configurations) where there is no instability induced at one loop and where the potential is exponentially suppressed thanks to a Bose/Fermi degeneracy at the massless level. Eventually, in heterotic string models, the backreaction of the one-loop potential generated by a spontaneous Scherk--Schwarz supersymmetry breaking on the cosmology is studied. Flat and ever-expanding solutions are looked for to establish if the classical cosmological dynamics of such solutions is perturbed or not by the one-loop quantum corrections. We then describe a new process for generating a non-relativistic dark-matter relic density in models with spontaneously broken supersymmetry and implementation of the finite temperature through compactification of the Euclidean time.L'objectif de cette thèse est d'explorer divers aspects de la théorie des cordes, théorie unificatrice de la matière et de toutes les interactions fondamentales incluant l'interaction gravitationnelle. Dans un premier chapitre, nous commençons par résumer quelques ingrédients clés de cette théorie et de sa construction pour motiver les travaux présentés dans ce manuscrit. Nous explorons ensuite trois facettes de la théorie des cordes. Dans un premier temps, nous définissons un nouveau mécanisme de brisure de supersymétrie dans des modèles de cordes ouvertes et nous en commentons les particularités en le mettant en perspective avec des mécanismes existants. Dans un second temps, nous étudions les masses à une boucle acquises par des modules en théorie des cordes de type I avec brisure N=2 N=0 de supersymétrie implémentée par un mécanisme de Scherk--Schwarz. Différentes stratégies sont utilisées pour conclure quant à la stabilité ou non de la grande diversité des modules présents dans le modèle. Cela passe par exemple par le calcul de l'expansion de Taylor au deuxième ordre du potentiel effectif, par l'évaluation de fonctions de corrélation à deux points à une boucle ou encore par l'utilisation d'arguments de dualité entre les cordes hétérotiques et la théorie des cordes de type I. Une fois toutes les masses évaluées, nous décrivons explicitement des modèles où aucune instabilité n'est générée et où le potentiel à une boucle est exponentiellement supprimé. Enfin, dans le cadre de modèles de cordes hétérotiques, nous étudions l'effet du potentiel à une boucle générée par une brisure de supersymétrie par mécanisme de Scherk-Schwarz sur la cosmologie. Nous recherchons des solutions d'espace-temps plat en éternelle expansion pour établir si la dynamique cosmologique de ces solutions au niveau classique est perturbée ou non. Nous explorons ensuite un nouveau processus pour générer une densité relique de matière noire non relativiste dans des modèles avec brisure de supersymétrie et implémentation de la température finie

String Phenomenology 2019

I will talk about a new scenario for generating a relic density of non-relativistic dark matter in the framework of heterotic string theory with spontaneously broken supersymmetry and at finite temperature. In this scenario, contrary to the standard thermal freeze-out process, dark-matter particles are produced while they are still relativistic and then decouple from the thermal bath because of a sudden increase of their mass above the universe temperature. The mass increase is sourced by the destabilization of a modulus triggered when the temperature of the universe drops below the supersymmetry breaking scale. This phase transition is enforced to take place in certain models thanks to a cosmological attractor mechanism

Moduli stability in type I string orbifold models

International audienceWe consider an open string orbifold model realizing the $\mathcal{N}=2\to \mathcal{N}=0$ spontaneous breaking of supersymmetry in four dimensional Minkowski spacetime. We show that in the region of moduli space where the supersymmetry breaking scale is lower than the other scales, there are tachyon free backgrounds with exponentially small effective potentials at one loop

One-loop masses of Neumann-Dirichlet open strings and boundary-changing vertex operators

International audienceWe derive the masses acquired at one loop by massless scalars in the Neumann-Dirichlet sector of open strings, when supersymmetry is spontaneously broken. It is done by computing two-point functions of “boundary-changing vertex operators” inserted on the boundaries of the annulus and Möbius strip. This requires the evaluation of correlators of “excited boundary-changing fields,” which are analogous to excited twist fields for closed strings. We work in the type IIB orientifold theory compactified on T$^{2}$× T$^{4}$/ℤ$_{2}$, where $\mathcal{N}$ = 2 supersymmetry is broken to $\mathcal{N}$ = 0 by the Scherk-Schwarz mechanism implemented along T$^{2}$. Even though the full expression of the squared masses is complicated, it reduces to a very simple form when the lowest scale of the background is the supersymmetry breaking scale M$_{3/2}$. We use our results to analyze in this regime the stability at the quantum level of the moduli fields arising in the Neumann-Dirichlet sector. This completes the study of ref. [32], where the quantum masses of all other types of moduli arising in the open- or closed-string sectors are derived. Ultimately, we identify all brane configurations that produce backgrounds without tachyons at one loop and yield an effective potential exponentially suppressed, or strictly positive with runaway behavior of M$_{3/2}$

Quantum no-scale regimes and moduli dynamics

International audienceWe analyze quantum no-scale regimes (QNSR) in perturbative heterotic string compactified on tori, with total spontaneous breaking of supersymmetry. We show that for marginal deformations initially at any point in moduli space, the dynamics of a flat, homogeneous and isotropic universe can always be attracted to a QNSR. This happens independently of the characteristics of the 1-loop effective potential V_1-loop , which can be initially positive, negative or vanishing, and maximal, minimal or at a saddle point. In all cases, the classical no-scale structure is restored at the quantum level, during the cosmological evolution. This is shown analytically by considering moduli evolutions entirely in the vicinity of their initial values. Global attractor mechanisms are analyzed numerically and depend drastically on the sign of V_1-loop. We find that all initially expanding cosmological evolutions along which V_1-loop is positive are attracted to the QNSR describing a flat, ever-expanding universe. On the contrary, when V_1-loop can reach negative values, the expansion comes to a halt and the universe eventually collapses into a Big Crunch, unless the initial conditions are tuned in a tiny region of the phase space. This suggests that flat, ever-expanding universes with positive potentials are way more natural than their counterparts with negative potentials

Two-point functions of Neumann–Dirichlet open-string sector moduli

International audienc

Corrigendum to “On the stability of open-string orbifold models with broken supersymmetry” [Nucl. Phys. B 957 (2020) 115100]

We consider an open-string realisation of N=2→N=0 spontaneous breaking of supersymmetry in four-dimensional Minkowski spacetime. It is based on type IIB orientifold theory compactified on T2×T4/Z2, with Scherk–Schwarz supersymmetry breaking implemented along T2. We show that in the regions of moduli space where the supersymmetry breaking scale is lower than the other scales, there exist configurations with minima that have massless Bose-Fermi degeneracy and hence vanishing one-loop effective potential, up to exponentially suppressed corrections. These backgrounds describe non-Abelian gauge theories, with all open-string moduli and blowing up modes of T4/Z2 stabilized, while all untwisted closed-string moduli remain flat directions. Other backgrounds with strictly positive effective potentials exist, where the only instabilities arising at one loop are associated with the supersymmetry breaking scale, which runs away. All of these backgrounds are consistent non-perturbatively