Hiroyuki Abe
We discuss the nature of sequestering supersymmetry breaking sectors in a certain class of moduli stabilization in supergravity/string models, where a negative vacuum energy of the nonperturbative moduli potential is canceled by dynamically generated F-terms. Two illustrating examples are shown to sketch the issues around the supersymmetry breaking, flavors and sequestering within such a framework.
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We study concretely several issues altogether, moduli stabilization, the dynamical supersymmetry (SUSY) breaking, the uplifting of SUSY anti-de Sitter (AdS) vacuum and the sequestering of hidden sector, in a simple supergravity model with a single extra dimension. The sequestering is achieved dynamically by a wavefunction localization in extra dimension. The expressions for the visible sector soft SUSY breaking terms as well as the hidden sector potential are shown explicitly in our model. We find that the tree-level soft scalar mass and the A-term can be suppressed at a SUSY breaking Minkowsk…
We study moduli stabilization with F-term uplifting. As a source of uplifting F-term, we consider spontaneous supersymmetry breaking models, e.g. the Polonyi model and the Intriligator-Seiberg-Shih model. We analyze potential minima by requiring almost vanishing vacuum energy and evaluate the size of modulus F-term. We also study soft SUSY breaking terms. In our scenario, the mirage mediation is dominant in gaugino masses. Scalar masses can be comparable with gaugino masses or much heavier, depending on couplings with spontaneous supersymmetry breaking sector.
We discuss the role of F-term uplifting in stabilizing moduli within the framework of heterotic string theory. It turns out that the uplifting sector plays an important role in fixing the volume modulus at one of the self-dual points of a modular invariant potential. For the volume modulus stabilized at a self-dual point, the F-term uplifting leads to the dilation stabilization which can naturally yield the mirage mediation pattern of soft supersymmetry breaking terms. Generalizing to the case with anomalous U(1) gauge symmetry, we also find that the U(1) sector generically gives a contributio…
We study Kähler moduli stabilization in IIB superstring theory. We propose a new moduli stabilization mechanism by the supersymmetry-braking chiral superfield which is coupled to Kähler moduli in Kähler potential. We also study uplifting of the Large Volume Scenario (LVS) by it. In both cases, the form of superpotential is crucial for moduli stabilization. We confirm that our uplifting mechanism does not destabilize the vacuum of the LVS drastically.
We study the mediation of supersymmetry breaking in string compactifications whose moduli are stabilized by nonperturbative effects. We begin with a critical review of arguments for sequestering in supergravity and in string theory. We then show that geometric isolation, even in a highly warped space, is insufficient to achieve sequestering: in type IIB compactifications, nonperturbative superpotentials involving the Kahler moduli introduce cross-couplings between well-separated visible and hidden sectors. The scale of the resulting soft terms depends on the moduli stabilization scenario. In t…
We study the possibility of using the D-term associated to an anomalous U(1) for the uplifting of AdS vacua (to dS or Minkowski vacua) in effective supergravities arising from string theories, particularly in the type IIB context put forward by Kachru, Kallosh, Linde and Trivedi (KKLT). We find a gauge invariant formulation of such a scenario (avoiding previous inconsistencies), where the anomalous D-term cannot be cancelled, thus triggering the uplifting of the vacua. Then, we examine the general conditions for this to happen. Finally, we illustrate the results by presenting different success…
We study sequestering, a prerequisite for flavor-blind supersymmetry breaking in several high-scale mediation mechanisms, in compactifications of type IIB string theory. We find that although sequestering is typically absent in unwarped backgrounds, strongly warped compactifications do readily sequester. The AdS/CFT dual description in terms of conformal sequestering plays an important role in our analysis, and we establish how sequestering works both on the gravity side and on the gauge theory side. We pay special attention to subtle compactification effects that can disrupt sequestering. Our…
We study moduli stabilization and a realization of de Sitter vacua in generalized F-term uplifting scenarios of the KKLT-type anti-de Sitter vacuum, where the uplifting sector X directly couples to the light Kähler modulus T in the superpotential through, e.g., stringy instanton effects. F-term uplifting can be achieved by a spontaneous supersymmetry breaking sector, e.g., the Polonyi model, the O'Raifeartaigh model and the Intriligator-Seiberg-Shih model. Several models with the X-T mixing are examined and qualitative features in most models {\it even with such mixing} are almost the same as …
We examine the pattern of soft supersymmetry breaking terms in moduli stabilization, where an uplifting potential is provided by spontaneously broken supersymmetry in a generic sequestered sector. From stationary conditions, we derive the relation between moduli F-term vacuum expectation values which does not depend on the details of sequestered uplifting. This moduli F-term relation is crucial for identifying the dominant source of soft terms of visible fields.
The issue of fine-tuning necessary to achieve satisfactory degree of hierarchy between moduli masses, the gravitino mass and the scale of the cosmological constant has been revisited in the context of supergravities with consistent D-terms. We have studied (extended) racetrack models where supersymmetry breaking and moduli stabilisation cannot be separated from each other. We show that even in such cases the realistic hierarchy can be achieved on the expense of a single fine-tuning. The presence of two condensates changes the role of the constant term in the superpotential, W_0, and solutions …
An important ingredient in the construction of phenomenologically viable superstring models is the uplifting of Anti-de Sitter supersymmetric critical points in the moduli sector to metastable Minkowski or de Sitter vacua with broken supersymmetry. In all cases described so far, uplifting results in a displacement of the potential minimum away from the critical point and, if the uplifting is large, can lead to the disappearance of the minimum altogether. We propose a variant of F-term uplifting which exactly preserves supersymmetric critical points and shift symmetries at tree level. In spite …
Moduli stabilization in the type IIA massive string theory so far was achieved only in the AdS vacua. The uplifting to dS vacua has not been performed as yet: neither the analogs of type IIB anti-D3 brane at the tip of the conifold, nor the appropriate D-terms have been identified. The hope was recently expressed that the F-term uplifting may work. We investigate this possibility in the context of a simplified version of the type IIA model developed in hep-th/0505160 and find that the F-term does not uplift the AdS vacua to dS vacua with positive CC. Thus it remains a challenging task to find …
In this note, we review our construction of de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D-term uplifting can be combined consistently with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kähler potential stabilize the volume Kahler modulus in an AdS_4-vacuum. Then, magnetized D7-branes provide consistent supersymmetric D-term uplifting towards dS_4. Based on hep-th/0602253.
We study in detail the stability properties of the simplest F-term uplifting mechanism consistent with the integration of heavy moduli. This way of uplifting vacua guarantees that the interaction of the uplifting sector with the moduli sector is consistent with integrating out the heavy fields in a supersymmetric way. The interactions between light and heavy fields are characterized in terms of the Kahler invariant function, G = K + log |W|^2, which is required to be separable in the two sectors. We generalize earlier results that when the heavy fields are stabilized at a minimum of the Kahler…
We analyse the effective supergravity model of a warped compactification with matter on D3 and D7-branes. We find that the main effect of the warp factor is to modify the F-terms while leaving the D-terms invariant. Hence warped models with moduli stabilisation and a small positive cosmological constant resulting from a large warping can only be achieved with an almost vanishing D-term and a F-term uplifting. By studying string-motivated examples with gaugino condensation on magnetised D7-branes, we find that even with a vanishing D-term, it is difficult to achieve a Minkowski minimum for reas…
We use the F-term dynamical supersymmetry breaking models with metastable vacua in order to uplift the vacuum energy in the KKLT moduli stabilization scenario. The main advantage compared to earlier proposals is the manifest supersymmetric treatment and the natural coexistence of a TeV gravitino mass with a zero cosmological constant. We argue that it is generically difficult to avoid anti de-Sitter supersymmetric minima, however the tunneling rate from the metastable vacuum with zero vacuum energy towards them can be very suppressed. We briefly comment on the properties of the induced soft te…
We study the scattering and sequestering of blow-up fields - either local to or distant from a visible matter sector - through a CFT computation of the dependence of physical Yukawa couplings on the blow-up moduli. For a visible sector of D3-branes on orbifold singularities we compute the disk correlator < τ_s^{(1)} τ_s^{(2)} ... τ_s^{(n)} ψψϕ> between orbifold blow-up moduli and matter Yukawa couplings. For n = 1 we determine the full quantum and classical correlator. This result has the correct factorisation onto lower 3-point functions and also passes numerous other consistency checks. For …
We develop a method for constructing metastable de Sitter vacua in N=1 supergravity models describing the no-scale volume moduli sector of Calabi-Yau string compactifications. We consider both heterotic and orientifold models. Our main guideline is the necessary condition for the existence of metastable vacua coming from the Goldstino multiplet, which constrains the allowed scalar geometries and supersymmetry-breaking directions. In the simplest non-trivial case where the volume is controlled by two moduli, this condition simplifies and turns out to be fully characterised by the intersection n…
We study the possibility of realizing an effective sequestering between visible and hidden sectors in generic heterotic string models, generalizing previous work on orbifold constructions to smooth Calabi-Yau compactifications. In these theories, genuine sequestering is spoiled by interactions mixing chiral multiplets of the two sectors in the effective Kahler potential. These effective interactions however have a specific current-current-like structure and can be interpreted from an M-theory viewpoint as coming from the exchange of heavy vector multiplets. One may then attempt to inhibit the …
The renormalization of operators responsible for soft supersymmetry breaking is usually calculated by starting at some high scale and including only visible sector interactions in the evolution equations, while ignoring hidden sector interactions. Here we explain why this is correct only for the most trivial structures in the hidden sector, and discuss possible implications. This investigation was prompted by the idea of conformal sequestering. In that framework hidden sector renormalizations by nearly conformal dynamics are critical. In the original models of conformal sequestering it was nec…
Effective potentials, warping, and implications for F-term uplifting
研究通过分析IIB弦理论反卷积中弯曲对标量势的修正，探讨其对Calabi-Yau反向折叠模型F项德西特抬升的影响，提出四维N=1超引力中的弯曲凯勒势，并指出在KKLT框架中经典弯曲修正及混合修正主导，而LVS构造中修正被体积倒数抑制。
We study the effect of anomalous U(1) gauge groups in string theory compactification with fluxes. We find that, in a gauge invariant formulation, consistent AdS vacua appear breaking spontaneously supergravity. Non vanishing D-terms from the anomalous symmetry act as an uplifting potential and could allow for de Sitter vacua. However, we show that in this case the gravitino is generically (but not always) much heavier than the electroweak scale. We show that alternative uplifting scheme based on corrections to the Kahler potential can be compatible with a gravitino mass in the TeV range.
We study supersymmetric models with double gaugino condensations in the hidden sector, where the gauge couplings depend on two light moduli of superstring theory. We perform a detailed analysis of this class of model and show that there is no stable supersymmetric minimum with finite vacuum values of moduli fields. Instead, we find that the supersymmetry breaking occurs with moduli stabilized and negative vacuum energy. That yields moduli-dominated soft supersymmetry breaking terms. To realize slightly positive (or vanishing) vacuum energy, we add uplifting potential. We discuss uplifting does…
Hidden sector D7-branes with non-zero gauge flux are a generic feature of type IIB compactifications. A non-vanishing Fayet-Iliopoulos term induced by non-zero gauge flux leads to a T-brane configuration. Expanding the D7-brane action around this T-brane background in the presence of three-form supersymmetry breaking fluxes, we obtain a positive definite contribution to the moduli scalar potential which can be used as an uplifting source for de Sitter vacua. In this way we provide a higher-dimensional understanding of known 4D mechanisms of de Sitter uplifting based on hidden sector F-terms wh…
It is shown that racetrack inflation can be implemented in a moduli stabilisation scenario with a supersymmetric uplifting D-term. The resulting model is completely described by an effective supergravity theory, in contrast to the original racetrack models. We study the inflationary dynamics and show that the gaugino condensates vary during inflation. The resulting spectral index is n_s = 0.95 as in the original racetrack inflation model. Hence extra fields do not appear to alter the predictions of the model. An equivalent, simplified model with just a single field is presented.
The KKLT construction of de Sitter vacua includes an uplifting term coming from an anti-D3-brane. Here we show how this term can arise via spontaneous breaking of supersymmetry, based on the emergence of a nilpotent chiral supermultiplet on the world-volume of the anti-D3-brane. We establish and use the fact that both the DBI as well as the WZ term, with account of orientifolding, acquire a form of the Volkov-Akulov action. For an O3 orientifold involution of $\mathbb{R}^{9,1}$ we demonstrate the cancellation between the fermionic parts of the DBI and WZ term for the D3-brane action. For the a…
We propose a supersymmetrisation of the cosmological constant in ordinary $N=1$ supergravity that breaks supersymmetry spontaneously by a constant Fayet-Iliopoulos (FI) term associated to a $U(1)$ symmetry. This term is a variation of a new gauge invariant FI term proposed recently, which is invariant under Kähler transformations and can be written even for a gauged R-symmetry on top of the standard FI contribution. The two terms are the same in the absence of matter but differ in its presence. The proposed term is reduced to a constant FI-term up to fermion interactions that disappear in the …
We present a D-term hybrid inflation model, embedded in supergravity with moduli stabilisation. Its novel features allow us to overcome the serious challenges of combining D-term inflation and moduli fields within the same string-motivated theory. One salient point of the model is the positive definite uplifting D-term arising from the moduli stabilisation sector. By coupling this D-term to the inflationary sector, we generate an effective Fayet-Iliopoulos term. Moduli corrections to the inflationary dynamics are also obtained. Successful inflation is achieved for a limited range of parameter …
We study dilaton stabilization in heterotic string models. By utilizing the asymmetric orbifold construction, we construct an explicit three-generation model whose matter content in the visible sector is the supersymmetric standard model with additional vectorlike matter. This model does not contain any geometric moduli fields except the dilaton field. Model building at a symmetry enhancement point in moduli space enlarges the rank of the hidden gauge group. By analyzing multiple hidden gauge sectors, the dilaton field is stabilized by the racetrack mechanism. We also discuss a supersymmetry b…
We study the influence of anomalous U(1) symmetries and their associated D-terms on the vacuum structure of global field theories once they are coupled to N=1 supergravity and in the context of string compactifications with moduli stabilisation. In particular, we focus on a IIB string motivated construction of the ISS scenario and examine the influence of one additional U(1) symmetry on the vacuum structure. We point out that in the simplest one-Kahler modulus compactification, the original ISS vacuum gets generically destabilised by a runaway behaviour of the potential in the modulus directio…
Consistent uplifting of AdS vacua in string theory often requires extra light degrees of freedom in addition to those of a (Kaehler) modulus. Here we consider the possibility that de Sitter and Minkowski vacua arise due to hidden sector matter interactions. We find that, in this scheme, the hierarchically small supersymmetry breaking scale can be explained by the scale of gaugino condensation and that interesting patterns of the soft terms arise. In particular, a matter-dominated supersymmetry breaking scenario and a version of the mirage mediation scheme appear in the framework of spontaneous…
We study supergravity models in four dimensions where the hidden sector is superconformal and strongly-coupled over several decades of energy below the Planck scale, before undergoing spontaneous breakdown of scale invariance and supersymmetry. We show that large anomalous dimensions can suppress Kahler contact terms between the hidden and visible sectors, leading to models in which the hidden sector is "sequestered" and anomaly-mediated supersymmetry breaking can naturally dominate, thus solving the supersymmetric flavor problem. We construct simple, explicit models of the hidden sector based…
We examine the effects of anomalous U(1)_A gauge symmetry on soft supersymmetry breaking terms while incorporating the stabilization of the modulus-axion multiplet responsible for the Green-Schwarz (GS) anomaly cancellation mechanism. In case of the KKLT stabilization of the GS modulus, soft terms are determined by the GS modulus mediation, the anomaly mediation and the U(1)_A mediation which are generically comparable to each other, thereby yielding the mirage mediation pattern of superparticle masses at low energy scale. Independently of the mechanism of moduli stabilization and supersymmetr…
We present a new way to construct de Sitter vacua in type IIB flux compactifications, in which moduli stabilization and D-term uplifting can be combined in a manner consistent with the supergravity constraints. Here, the closed string fluxes fix the dilaton and the complex structure moduli while perturbative quantum corrections to the Kahler potential stabilize the volume Kahler modulus in an AdS_4-vacuum. Then, the presence of magnetized D7-branes in this setup provide supersymmetric D-terms in a fully consistent way which uplift the AdS_4-vacuum to a metastable dS-minimum.
Sequestered String Models imply Split Supersymmetry
本文研究了隔离弦模型的稳定性界限和味道约束，发现满足条件需软项产生TeV级规范子和约10^7 GeV标量费米子的分裂超对称质量谱，否则会面临味道改变或真空稳定性问题。
We study the effective field theory of KKLT and LVS moduli stabilisation scenarios coupled to an anti-D3-brane at the tip of a warped throat. We describe the presence of the anti-brane in terms of a nilpotent goldstino superfield in a supersymmetric effective field theory. The introduction of this superfield produces a term that can lead to a de Sitter minimum. We fix the Kaehler moduli dependence of the nilpotent field couplings by matching this term with the anti-D3-brane uplifting contribution. The main result of this paper is the computation, within this EFT, of the soft supersymmetry brea…
We investigate neutralino dark matter from a string/M-theory perspective. Using the Kallosh-Linde (KL) scenario to stabilize the string moduli requires supersymmetry breaking for uplifting to a de Sitter vacuum. We consider the free magnetic dual description of $\mathcal{N}=1$ SUSY QCD with massive flavours, the Intriligator-Seiberg-Shih model (ISS), as an F-term dynamical SUSY breaking sector. This framework allows for a gravitino mass in the TeV range. Moreover, due to the plethora of particles from the ISS sector, we investigate the consequences of coupling the MSSM with the KL-ISS setup to…
We describe the resulting phenomenology of string theory/supergravity models with strong moduli stabilization. The KL model with F-term uplifting, is one such example. Models of this type predict universal scalar masses equal to the gravitino mass. In contrast, A-terms receive highly suppressed gravity mediated contributions. Under certain conditions, the same conclusion is valid for gaugino masses, which like A-terms, are then determined by anomalies. In such models, we are forced to relatively large gravitino masses (30-1000 TeV). We compute the low energy spectrum as a function of m_{3/2}. …
We examine recent work on compactifications of string theory with fluxes, where effective potentials for light moduli have been derived after integrating out moduli that are assumed to be heavy at the classical level, and then adding non-perturbative (NP) corrections to the superpotential. We find that this two stage procedure is not valid and that the correct potential has additional terms. Althought this does not affect the conclusion of Kachru et al (KKLT) that the Kaehler moduli may be stabilized by NP effects, it can affect the detailed physics. In particular it is possible to get metasta…
In the present paper, we reexamine the moduli stabilization problem of the Type IIB orientifolds with one complex structure modulus in a modified two-step procedure. The full superpotential including both the 3-form fluxes and the non-perturbative corrections is used to yield a F-term potential. This potential is simplified by using one optimization condition to integrate the dilaton field out. It is shown that having a locally stable supersymmetric Anti-deSitter vacuum is not inevitable for these orientifolds, which depend strongly upon the details of the flux parameters. For those orientifol…
The $N=1$ supersymmetric Born-Infeld theory coupled to $N=1$ supergravity in four spacetime dimensions is studied in the presence of a cosmological term with spontaneous supersymmetry breaking. The consistency is achieved by compensating a negative contribution to the cosmological term from the Born-Infeld theory by a positive contribution originating from the gravitino condensate. This leads to an identification of the Born-Infeld scale with the supersymmetry breaking scale. The dynamical formation of the gravitino condensate in supergravity is reconsidered and the induced one-loop effective …
Anti-D3 branes and non-perturbative effects in flux compactifications spontaneously break supersymmetry and stabilise moduli in a metastable de Sitter vacua. The low energy 4D effective field theory description for such models would be a supergravity theory with non-linearly realised supersymmetry. Guided by string theory modular symmetry, we compute this non-linear supergravity theory, including dependence on all bulk moduli. Using either a constrained chiral superfield or a constrained vector field, the uplifting contribution to the scalar potential from the anti-D3 brane can be parameterise…
We analyze the interplay between Kähler moduli stabilization and chaotic inflation in supergravity. While heavy moduli decouple from inflation in the supersymmetric limit, supersymmetry breaking generically introduces non-decoupling effects. These lead to inflation driven by a soft mass term, $m_φ^2 \sim m m_{3/2}$, where $m$ is a supersymmetric mass parameter. This scenario needs no stabilizer field, but the stability of moduli during inflation imposes a large supersymmetry breaking scale, $m_{3/2} \gg H$, and a careful choice of initial conditions. This is illustrated in three prominent exam…
We perform a general study about the existence of non-supersymmetric minima with vanishing cosmological constant in supergravity models involving only chiral superfields. We study the conditions under which the matrix of second derivatives of the scalar potential is positive definite. We show that there exist very simple and strong necessary conditions for stability that constrain the Kahler curvature and the ratios of the supersymmetry-breaking auxiliary fields defining the Goldstino direction. We then derive more explicitly the implications of these constraints in the case where the Kahler p…
F-theory compactifications on Calabi-Yau fivefolds give rise to two-dimensional N=(0,2) supersymmetric field theories coupled to gravity. We explore the dilaton supergravity defined by the moduli sector of such compactifications. The massless moduli spectrum is found by uplifting Type IIB compactifications on Calabi-Yau fourfolds. This spectrum matches expectations from duality with M-theory on the same elliptic fibration. The latter defines an N=2 Supersymmetric Quantum Mechanics related to the 2d (0,2) F-theory supergravity via circle reduction. Using our recent results on the gravitational …
In the context of type IIB string theory we combine moduli stabilisation and model building on branes at del Pezzo singularities in a fully consistent global compactification. By means of toric geometry, we classify all the CY manifolds with 3 < h11 < 6 which admit two identical del Pezzo singularities mapped into each other under the orientifold involution. This effective singularity hosts the visible sector containing the Standard Model while the Kaehler moduli are stabilised via a combination of D-terms, perturbative and non-perturbative effects supported on hidden sectors. We present concr…
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