Ahler Moduli Research Articles

Generic no-scale inflation inspired from string theory compactifications

We propose the generic no-scale inflation inspired from string theory compactifications. We consider the K\"ahler potentials with an inflaton field $\ensuremath{\varphi}$, as well as one, two, and three K\"ahler moduli. Also, we consider the renormalizable superpotential of $\ensuremath{\varphi}$ in general. We study the spectral index and tensor-to-scalar ratio in details, and find the viable parameter spaces which are consistent with the Planck and BICEP/Keck experimental data on the cosmic microwave background (CMB). The spectral index is ${n}_{s}\ensuremath{\simeq}1\ensuremath{-}2/N\ensuremath{\sim}0.965$ for all models, and the tensor-to-scalar ratio $r$ is $r\ensuremath{\simeq}12/{N}^{2}$, $83/{N}^{4}$ and $4/{N}^{2}$ for the one, two and three moduli models, respectively. The particular $r$ for two moduli model comes from the contributions of the non-negligible higher order term in potential. In the three moduli model, the scalar potential is similar to the global supersymmetry, but the K\"ahler potential is different. The E model with $\ensuremath{\alpha}=1$ and T model with $\ensuremath{\alpha}=1/3$ can be realized in the one modulus model and the three moduli model, respectively. Interestingly, the models with quadratic and quartic potentials still satisfy the current tight bound on $r$ after embedding into no-scale supergravity.

Integer conformal dimensions for type IIa flux vacua

We give a concise argument that supersymmetric anti--de Sitter type IIA DeWolfe-Giryavets-Kachru-Taylor flux vacua on general Calabi-Yau's have, interpreted holographically, integer conformal dimensions for low-lying scalar primaries in the dual conformal field theory. These integers are independent of any compactification details, such as the background fluxes or triple intersection numbers of the compact manifold. For the K\"ahler moduli and dilaton, there is one operator with $\mathrm{\ensuremath{\Delta}}=10$ and ${h}_{\ensuremath{-}}^{1,1}$ operators with $\mathrm{\ensuremath{\Delta}}=6$, whereas the corresponding axions have $\mathrm{\ensuremath{\Delta}}=11$ and $\mathrm{\ensuremath{\Delta}}=5$. For the complex structure moduli, the ${h}^{2,1}$ saxions have $\mathrm{\ensuremath{\Delta}}=2$, and the axions $\mathrm{\ensuremath{\Delta}}=3$. We give a tentative discussion of the origin of these integers and effects that would modify these results.

Radiative Kähler moduli stabilization

We propose a new type of K\"ahler moduli stabilization mechanisms in type IIB superstring theory on Calabi-Yau manifolds with the positive Euler number. The overall K\"ahler modulus can be perturbatively stabilized by radiative corrections due to sparticles. Its minimum is the anti-de Sitter vacuum, where supersymmetry is broken. We can uplift it to the de Sitter vacuum by introducing anti-D-branes, keeping the modulus stabilized. Although our numerical results depend on the choice of the cutoff scale and degeneracies of sparticles, at any rate there exist the parameter spaces where the masses of Kaluza-Klein and stringy modes are larger than the cutoff scale. Furthermore, this stabilization scenario predicts an ultralight axion.

No inflation in type IIA strings on rigid Calabi–Yau spaces

We investigate whether cosmological inflation is possible in a class of flux compactifications of type IIA strings on rigid Calabi-Yau manifolds, when all perturbative string corrections are taken into account. We confine ourselves to the universal hypermultiplet and an abelian vector multiplet, representing matter in four dimensions. Since all axions can be stabilized by D-instantons, we choose dilaton and a K\"ahler modulus as the only running scalars. Though positivity of their scalar potential can be achieved, we find that there is no slow roll ($\varepsilon > 2$ and $\eta >2$), and no Graceful Exit because the scalar potential has the run-away behaviour resulting in decompactification. We conclude that it is impossible to generate phenomenologically viable inflation in the given class of flux compactifications of type IIA strings, without explicit breaking of $N=2$ local supersymmetry of the low-energy effective action.

Kähler moduli stabilization in semirealistic magnetized orbifold models

We study K\"ahler moduli stabilizations in semi-realistic magnetized D-brane models based on $ Z_2\times Z_2'$ toroidal orbifolds. In type IIB compactifications, 3-form fluxes can stabilize the dilaton and complex structure moduli fields, but there remain some massless closed string moduli fields, K\"ahler moduli. The magnetic fluxes generate Fayet-Iliopoulos terms, which can fix ratios of K\"ahler moduli. On top of that, we consider D-brane instanton effects to stabilize them in concrete D-brane models and investigate the brane configurations to confirm that the moduli fields can be stabilized successfully. In this paper, we treat two types of D-brane models. One is based on D9-brane systems respecting the Pati-Salam model. The other is realized in a D7-brane system breaking the Pati-Salam gauge group. We find suitable configurations where the D-brane instantons can stabilize the moduli fields within both types of D-brane models, explaining an origin of a small constant term of the superpotential which is a key ingredient for successful moduli stabilizations.

Reading off the nongeometric scalar potentials via the topological data of the compactifying Calabi-Yau manifolds

In the context of studying the 4D-effective potentials of type IIB nongeometric flux compactifications, this article has a twofold goal. First, we present a modular invariant symplectic rearrangement of the tree level nongeometric scalar potential arising from a flux superpotential which includes the S-dual pairs of nongeometric fluxes ($Q$, $P$), the standard NS-NS and RR three-form fluxes (${F}_{3}$, ${H}_{3}$), and the geometric flux ($\ensuremath{\omega}$). This ``symplectic formulation'' is valid for arbitrary numbers of K\"ahler moduli, and the complex structure moduli which are implicitly encoded in a set of symplectic matrices. In the second part, we further explicitly rewrite all the symplectic ingredients in terms of saxionic and axionic components of the complex structure moduli. The same leads to a compact form of the generic scalar potential being explicitly written out in terms of all the real moduli/axions. Moreover, the final form of the scalar potential needs only the knowledge of some topological data (such as Hodge numbers and the triple-intersection numbers) of the compactifying threefolds and their respective mirrors. Finally, we demonstrate how the same is equivalent to say that, for a given concrete example, various pieces of the scalar potential can be directly read off from our generic proposal, without the need of starting from the K\"ahler and superpotentials.

Challenges for D-brane large-field inflation with stabilizer fields

We study possible string theory compactifications which, in the low-energy limit, describe chaotic inflation with a stabilizer field. We first analyze type IIA setups where the inflationary potential arises from a D6-brane wrapping an internal three-cycle, and where the stabilizer field is either an open-string or bulk K\"ahler modulus. We find that after integrating out the relevant closed-string moduli consistently, tachyonic directions arise during inflation which cannot be lifted. This is ultimately due to the shift symmetries of the type IIA K\"ahler potential at large compactification volume. This motivates us to search for stabilizer candidates in the complex structure sector of type IIB orientifolds, since these fields couple to D7-brane Wilson lines and their shift symmetries are generically broken away from the large complex structure limit. However, we find that in these setups the challenge is to obtain the necessary hierarchy between the inflationary and Kaluza-Klein scales.

Axion decay constants away from the lamppost

It is unknown whether a bound on axion field ranges exists within quantum gravity. We study axion field ranges using extended supersymmetry, in particular allowing an analysis within strongly coupled regions of moduli space. We apply this strategy to Calabi-Yau compactifications with one and two K\"ahler moduli. We relate the maximally allowable decay constant to geometric properties of the underlying Calabi-Yau geometry. In all examples we find a maximal field range close to the reduced Planck mass (with the largest field range being 3.25 $M_P$). On this perspective, field ranges relate to the intersection and instanton numbers of the underlying Calabi-Yau geometry.

Universal properties of type IIB and F-theory flux compactifications at large complex structure

We consider flux compactifications of type IIB string theory and F-theory in which the respective superpotentials at large complex structure are dominated by cubic or quartic terms in the complex structure moduli. In this limit, the low-energy effective theory for the complex structure and axio-dilaton sector exhibits universal properties that are insensitive to the details of the compactification manifold or the flux configuration. We show that there are no vacua in this region and the spectrum of the Hessian matrix is highly peaked and consists only of three distinct eigenvalues ($0$, $2m_{3/2}^2$ and $8m_{3/2}^2$), independently of the number of moduli. We briefly comment on how the inclusion of K\"ahler moduli affect these findings. Our results generalise those of Brodie & Marsh [1], in which these universal properties were found in a subspace of the large complex structure limit of type IIB compactifications.

Natural inflation with and without modulations in type IIB string theory

We propose a mechanism for the natural inflation with and without modulation in the framework of type IIB string theory on toroidal orientifold or orbifold. We explicitly construct the stabilization potential of complex structure, dilaton and K\"ahler moduli, where one of the imaginary component of complex structure moduli becomes light which is identified as the inflaton. The inflaton potential is generated by the gaugino-condensation term which receives the one-loop threshold corrections determined by the field value of complex structure moduli and the axion decay constant of inflaton is enhanced by the inverse of one-loop factor. We also find the threshold corrections can also induce the modulations to the original scalar potential for the natural inflation. Depending on these modulations, we can predict several sizes of tensor-to-scalar ratio as well as the other cosmological observables reported by WMAP, Planck and/or BICEP2 collaborations.

ANOMALY STRUCTURE OF REGULARIZED SUPERGRAVITY

On-shell Pauli-Villars regularization of the one-loop divergences of supergravity theories is used to study the anomaly structure of supergravity and the cancellation of field theory anomalies under a $U(1)$ gauge transformation and under the T-duality group of modular transformations in effective supergravity theories with three K\"ahler moduli $T^i$ obtained from orbifold compactification of the weakly coupled heterotic string. This procedure requires constraints on the chiral matter representations of the gauge group that are consistent with known results from orbifold compactifications. Pauli-Villars regulator fields allow for the cancellation of all quadratic and logarithmic divergences, as well as most linear divergences. If all linear divergences were canceled, the theory would be anomaly free, with noninvariance of the action arising only from Pauli-Villars masses. However there are linear divergences associated with nonrenormalizable gravitino/gaugino interactions that cannot be canceled by PV fields. The resulting chiral anomaly forms a supermultiplet with the corresponding conformal anomaly, provided the ultraviolet cut-off has the appropriate field dependence, in which case total derivative terms, such as Gauss-Bonnet, do not drop out from the effective action. The anomalies can be partially canceled by the four-dimensional version of the Green-Schwarz mechanism, but additional counterterms, and/or a more elaborate set of Pauli-Villars fields and couplings, are needed to cancel the full anomaly, including D-term contributions to the conformal anomaly that are nonlinear in the parameters of the anomalous transformations.

Aligned natural inflation and moduli stabilization from anomalous U(1) gauge symmetries

To obtain natural inflation with large tensor-to-scalar ratio in string framework, we need a special moduli stabilization mechanism which can separate the masses of real and imaginary components of K\"ahler moduli at different scales, and achieve a trans-Planckian axion decay constant from sub-Planckian axion decay constants. In this work, we stabilize the matter fields by F-terms and the real components of K\"ahler moduli by D-terms of two anomalous $U(1)_X\times U(1)_A$ symmetries strongly at high scales, while the corresponding axions remain light due to their independence on the Fayet-Iliopoulos (FI) term in moduli stabilization. The racetrack-type axion superpotential is obtained from gaugino condensations of the hidden gauge symmetries $SU(n)\times SU(m)$ with massive matter fields in the bi-fundamental respresentations. The axion alignment via Kim-Nilles-Pelroso (KNP) mechanism corresponds to an approximate $S_2$ exchange symmetry of two K\"ahler moduli in our model, and a slightly $S_2$ symmetry breaking leads to the natural inflation with super-Planckian decay constant.

Natural inflation with natural trans-planckian axion decay constant from anomalous U(1) X

We propose a natural inflation model driven by an imaginary or axionic component of a K\"ahler modulus in string-inspired supergravity. The shift symmetry of the axion is gauged under an anomalous $U(1)_X$ symmetry, which leads to a modulus-dependent Fayet-Iliopoulos (FI) term. The matter fields are stabilized by F-terms, and the real component of the modulus is stabilized by the $U(1)_X$ D-term, while its axion remains light. Therefore, the masses of real and imaginary components of the modulus are separated at different scales. The scalar potential for natural inflation is realized by the superpotential from the non-perturbative effects. The trans-Planckian axion decay constant, which is needed to fit with BICEP2 observations, can be obtained naturally in this model.

Mirage models confront the LHC. II. Flux-stabilized type IIB string theory

We continue the study of a class of string-motivated effective supergravity theories in light of current data from the CERN Large Hadron Collider (LHC). In this installment we consider type IIB string theory compactified on a Calabi-Yau orientifold in the presence of fluxes, in the manner originally formulated by Kachru et al. We allow for a variety of potential uplift mechanisms and embeddings of the Standard Model field content into $D3$-and $D7$-brane configurations. We find that an uplift sector independent of the K\"ahler moduli, as is the case with anti-$D3$-branes, is inconsistent with data unless the matter and Higgs sectors are localized on $D7$ branes exclusively, or are confined to twisted sectors between $D3$-and $D7$-branes. We identify regions of parameter space for all possible $D$-brane configurations that remain consistent with Planck observations on the dark matter relic density and measurements of the $CP$-even Higgs mass at the LHC. Constraints arising from LHC searches at $\sqrt{s}=8\text{ }\text{ }\mathrm{TeV}$ and the LUX dark matter detection experiment are discussed. The discovery prospects for the remaining parameter space at dark matter direct-detection experiments are described, and signatures for detection of superpartners at the LHC with $\sqrt{s}=14\text{ }\text{ }\mathrm{TeV}$ are analyzed.

Slow-roll inflation in non-geometric flux compactification

By implementing a genetic algorithm we search for stable vacua in Type IIB non-geometric flux compactification on an isotropic torus with orientifold 3-planes. We find that the number of stable dS and AdS vacua are of the same order. Moreover we find that in all dS vacua the multi-field slow-roll inflationary conditions are fulfilled. Specifically we observe that inflation is driven by the axio-dilaton and the K\"ahler moduli. We also comment on the existence of one stable dS vacuum in the presence of exotic orientifolds.

G-flux, M5 instantons, andU(1)symmetries inF-theory

Local aspects of singular $F$-theory compactifications for supersymmetric grand unified theory model building are fairly well understood in terms of Higgs bundles and their spectral data. Several global issues remain, however, including a description of $G$-fluxes, which are key to constructing chiral matter and stabilizing moduli, and the global realization of $U(1)$ symmetries that can forbid phenomenologically unfavorable couplings. In this paper, we sharpen our earlier proposal for describing $G$-fluxes and $U(1)$s through a distinguished ``Tate'' divisor. As an application, we give a general discussion of M5-instanton contributions in the presence of $G$-flux and exemplify this in a concrete example, where we comment on the ability of instanton-induced superpotential couplings to stabilize K\"ahler moduli.

Superpotential de-sequestering in string models

Non-perturbative superpotential cross-couplings between visible sector matter and K\"ahler moduli can lead to significant flavour-changing neutral currents in compactifications of type IIB string theory. Here, we compute corrections to Yukawa couplings in orbifold models with chiral matter localised on D3-branes and non-perturbative effects on distant D7-branes. By evaluating a threshold correction to the D7-brane gauge coupling, we determine conditions under which the non-perturbative corrections to the Yukawa couplings appear. The flavour structure of the induced Yukawa coupling generically fails to be aligned with the tree-flavour structure. We check our results by also evaluating a correlation function of two D7-brane gauginos and a D3-brane Yukawa coupling. Finally, by calculating a string amplitude between n hidden scalars and visible matter we show how non-vanishing vacuum expectation values of distant D7-brane scalars, if present, may correct visible Yukawa couplings with a flavour structure that differs from the tree-level flavour structure.

Kinetic mixing of U(1)’s for local string models

We study kinetic mixing between massless U(1)s in toroidal orbifolds with D3-branes at orbifold singularities. We focus in particular on C^3/Z_4 singularities but also study C^3/Z_6 and C^3/Z'_6 singularities. We find kinetic mixing can be present and describe the conditions for it to occur. Kinetic mixing comes from winding modes in the N=2 sector of the orbifold. If kinetic mixing is present its size depends only on the complex structure modulus of the torus and is independent of the K\"ahler moduli. We also study gauge threshold corrections for local Z_M x Z_N orbifold models finding that, consistent with previous studies, gauge couplings run from the bulk winding scale rather than the string scale.

Heterotic flux attractors

We find attractor equations describing moduli stabilization for heterotic compactifications with generic SU(3)-structure. Complex structure and K\"ahler moduli are treated on equal footing by using SU(3)xSU(3)-structure at intermediate steps. All independent vacuum data, including VEVs of the stabilized moduli, is encoded in a pair of generating functions that depend on fluxes alone. We work out an explicit example that illustrates our methods.

Low-scale inflation and supersymmetry breaking in racetrack models

In many moduli stabilization schemes in string theory, the scale of inflation appears to be of the same order as the scale of supersymmetry breaking. For low-scale supersymmetry breaking, therefore, the scale of inflation should also be low, unless this correlation is avoided in specific models. We explore such a low-scale inflationary scenario in a racetrack model with a single modulus in type IIB string theory. Inflation occurs near a point of inflection in the K\"ahler modulus potential. Obtaining acceptable cosmological density perturbations leads to the introduction of magnetized D7-branes sourcing non-perturbative superpotentials. The gravitino mass, m_{3/2}, is chosen to be around 30 TeV, so that gravitinos that are produced in the inflaton decay do not affect big-bang nucleosynthesis. Supersymmetry is communicated to the visible sector by a mixture of anomaly and modulus mediation. We find that the two sources contribute equally to the gaugino masses, while scalar masses are decided mainly by anomaly contribution. This happens as a result of the low scale of inflation and can be probed at the LHC.