Systematics of String Loop Corrections in Type IIB Calabi-Yau Flux Compactifications

We study the behaviour of the string loop corrections to the N=1 4D supergravity Kaehler potential that occur in flux compactifications of IIB string theory on general Calabi-Yau three-folds. We give a low energy interpretation for the conjecture of Berg, Haack and Pajer for the form of the loop corrections to the Kaehler potential. We check the consistency of this interpretation in several examples. We show that for arbitrary Calabi-Yaus, the leading contribution of these corrections to the scalar potential is always vanishing, giving an "extended no-scale structure". This result holds as long as the corrections are homogeneous functions of degree -2 in the 2-cycle volumes. We use the Coleman-Weinberg potential to motivate this cancellation from the viewpoint of low-energy field theory. Finally we give a simple formula for the 1-loop correction to the scalar potential in terms of the tree-level Kaehler metric and the correction to the Kaehler potential. We illustrate our ideas with several examples. A companion paper will use these results in the study of Kaehler moduli stabilisation.Comment: 34 pages and 3 figures; typos corrected and references adde

Scanning the Landscape of Flux Compactifications: Vacuum Structure and Soft Supersymmetry Breaking

We scan the landscape of flux compactifications for the Calabi-Yau manifold $\mathbb{P}^4_{[1,1,1,6,9]}$ with two K\" ahler moduli by varying the value of the flux superpotential $W_0$ over a large range of values. We do not include uplift terms. We find a rich phase structure of AdS and dS vacua. Starting with $W_0\sim 1$ we reproduce the exponentially large volume scenario, but as $W_0$ is reduced new classes of minima appear. One of them corresponds to the supersymmetric KKLT vacuum while the other is a new, deeper non-supersymmetric minimum. We study how the bare cosmological constant and the soft supersymmetry breaking parameters for matter on D7 branes depend on $W_0$, for these classes of minima. We discuss potential applications of our results.Comment: draft format remove

Fibre Inflation: Observable Gravity Waves from IIB String Compactifications

We introduce a simple string model of inflation, in which the inflaton field can take trans-Planckian values while driving a period of slow-roll inflation. This leads naturally to a realisation of large field inflation, inasmuch as the inflationary epoch is well described by the single-field scalar potential $V = V_0 (3-4 e^{-\hat\varphi/\sqrt{3}})$. Remarkably, for a broad class of vacua all adjustable parameters enter only through the overall coefficient $V_0$, and in particular do not enter into the slow-roll parameters. Consequently these are determined purely by the number of \e-foldings, $N_e$, and so are not independent: $\varepsilon \simeq \frac32 \eta^2$. This implies similar relations among observables like the primordial scalar-to-tensor amplitude, $r$, and the scalar spectral tilt, $n_s$: $r \simeq 6(n_s - 1)^2$. $N_e$ is itself more model-dependent since it depends partly on the post-inflationary reheat history. In a simple reheating scenario a reheating temperature of $T_{rh}\simeq 10^{9}$ GeV gives $N_e\simeq 58$, corresponding to $n_s\simeq 0.970$ and $r\simeq 0.005$, within reach of future observations. The model is an example of a class that arises naturally in the context of type IIB string compactifications with large-volume moduli stabilisation, and takes advantage of the generic existence there of Kahler moduli whose dominant appearance in the scalar potential arises from string loop corrections to the Kahler potential. The inflaton field is a combination of Kahler moduli of a K3-fibered Calabi-Yau manifold. We believe there are likely to be a great number of models in this class -- `high-fibre models' -- in which the inflaton starts off far enough up the fibre to produce observably large primordial gravity waves.Comment: Extended calculations beyond the leading approximations, including numerical integrations of multi-field evolution; Display an example with $r = 0.01$; Simplify the discussion of large fields; Corrected minor errors and typos; Added references; 41 pages LaTeX, 25 figure

Gaugino and Scalar Masses in the Landscape

In this letter we demonstrate the genericity of suppressed gaugino masses M_a \sim m_{3/2}/ln(M_P/m_{3/2}) in the IIB string landscape, by showing that this relation holds for D7-brane gauginos whenever the associated modulus is stabilised by nonperturbative effects. Although m_{3/2} and M_a take many different values across the landscape, the above small mass hierarchy is maintained. We show that it is valid for models with an arbitrary number of moduli and applies to both the KKLT and exponentially large volume approaches to Kahler moduli stabilisation. In the latter case we explicitly calculate gaugino and moduli masses for compactifications on the two-modulus Calabi-Yau P^4_[1,1,1,6,9]. In the large-volume scenario we also show that soft scalar masses are approximately universal with m_i^2 \sim m_{3/2}^2 (1 + \epsilon_i), with the non-universality parametrised by \epsilon_i \sim 1/ln (M_P/m_{3/2})^2 \sim 1/1000. We briefly discuss possible phenomenological implications of our results.Comment: 15 pages, JHEP style; v2. reference adde

Metastable SUSY Breaking, de Sitter Moduli Stabilisation and K\"ahler Moduli Inflation

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 direction. In more general compactifications with several Kahler moduli, we find a novel realisation of the LARGE volume scenario with D-term uplifting to de Sitter space and both D-term and F-term supersymmetry breaking. The structure of soft supersymmetry breaking terms is determined in the preferred scenario where the standard model cycle is not stabilised non-perturbatively and found to be flavour universal. Our scenario also provides a purely supersymmetric realisation of Kahler moduli (blow-up and fibre) inflation, with similar observational properties as the original proposals but without the need to include an extra (non-SUSY) uplifting term.Comment: 38 pages, 8 figures. v2: references added, minor correction

Systematics of Moduli Stabilization, Inflationary Dynamics and Power Spectrum

We study the scalar sector of type IIB superstring theory compactified on Calabi-Yau orientifolds as a place to find a mechanism of inflation in the early universe. In the large volume limit, one can stabilize the moduli in stages using perturbative method. We relate the systematics of moduli stabilization with methods to reduce the number of possible inflatons, which in turn lead to a simpler inflation analysis. Calculating the order-of-magnitude of terms in the equation of motion, we show that the methods are in fact valid. We then give the examples where these methods are used in the literature. We also show that there are effects of non-inflaton scalar fields on the scalar power spectrum. For one of the two methods, these effects can be observed with the current precision in experiments, while for the other method, the effects might never be observable.Comment: 20 pages, JHEP style; v.2 and v.3: typos fixed, discussion and references adde

Natural Quintessence in String Theory

We introduce a natural model of quintessence in string theory where the light rolling scalar is radiatively stable and couples to Standard Model matter with weaker-than- Planckian strength. The model is embedded in an anisotropic type IIB compactification with two exponentially large extra dimensions and TeV-scale gravity. The bulk turns out to be nearly supersymmetric since the scale of the gravitino mass is of the order of the observed value of the cosmological constant. The quintessence field is a modulus parameterising the size of an internal four-cycle which naturally develops a potential of the order (gravitino mass)^4, leading to a small dark energy scale without tunings. The mass of the quintessence field is also radiatively stable since it is protected by supersymmetry in the bulk. Moreover, this light scalar couples to ordinary matter via its mixing with the volume mode. Due to the fact that the quintessence field is a flat direction at leading order, this mixing is very small, resulting in a suppressed coupling to Standard Model particles which avoids stringent fifth-force constraints. On the other hand, if dark matter is realised in terms of Kaluza-Klein states, unsuppressed couplings between dark energy and dark matter can emerge, leading to a scenario of coupled quintessence within string theory. We study the dynamics of quintessence in our set-up, showing that its main features make it compatible with observations.Comment: 26 page

Gauge Threshold Corrections for Local String Models

We study gauge threshold corrections for local brane models embedded in a large compact space. A large bulk volume gives important contributions to the Konishi and super-Weyl anomalies and the effective field theory analysis implies the unification scale should be enhanced in a model-independent way from M_s to R M_s. For local D3/D3 models this result is supported by the explicit string computations. In this case the scale R M_s comes from the necessity of global cancellation of RR tadpoles sourced by the local model. We also study D3/D7 models and discuss discrepancies with the effective field theory analysis. We comment on phenomenological implications for gauge coupling unification and for the GUT scale.Comment: 30 pages; v2: references added, minor typos correcte

LARGE Volume String Compactifications at Finite Temperature

We present a detailed study of the finite-temperature behaviour of the LARGE Volume type IIB flux compactifications. We show that certain moduli can thermalise at high temperatures. Despite that, their contribution to the finite-temperature effective potential is always negligible and the latter has a runaway behaviour. We compute the maximal temperature $T_{max}$, above which the internal space decompactifies, as well as the temperature $T_*$, that is reached after the decay of the heaviest moduli. The natural constraint $T_*<T_{max}$ implies a lower bound on the allowed values of the internal volume $\mathcal{V}$. We find that this restriction rules out a significant range of values corresponding to smaller volumes of the order $\mathcal{V}\sim 10^{4}l_s^6$, which lead to standard GUT theories. Instead, the bound favours values of the order $\mathcal{V}\sim 10^{15}l_s^6$, which lead to TeV scale SUSY desirable for solving the hierarchy problem. Moreover, our result favours low-energy inflationary scenarios with density perturbations generated by a field, which is not the inflaton. In such a scenario, one could achieve both inflation and TeV-scale SUSY, although gravity waves would not be observable. Finally, we pose a two-fold challenge for the solution of the cosmological moduli problem. First, we show that the heavy moduli decay before they can begin to dominate the energy density of the Universe. Hence they are not able to dilute any unwanted relics. And second, we argue that, in order to obtain thermal inflation in the closed string moduli sector, one needs to go beyond the present EFT description.Comment: 54 pages + appendix, 5 figures; v2: minor corrections, references and footnotes added, version published on JCA

Towards Realistic String Vacua From Branes At Singularities

We report on progress towards constructing string models incorporating both realistic D-brane matter content and moduli stabilisation with dynamical low-scale supersymmetry breaking. The general framework is that of local D-brane models embedded into the LARGE volume approach to moduli stabilisation. We review quiver theories on del Pezzo $n$ ($dP_n$) singularities including both D3 and D7 branes. We provide supersymmetric examples with three quark/lepton families and the gauge symmetries of the Standard, Left-Right Symmetric, Pati-Salam and Trinification models, without unwanted chiral exotics. We describe how the singularity structure leads to family symmetries governing the Yukawa couplings which may give mass hierarchies among the different generations. We outline how these models can be embedded into compact Calabi-Yau compactifications with LARGE volume moduli stabilisation, and state the minimal conditions for this to be possible. We study the general structure of soft supersymmetry breaking. At the singularity all leading order contributions to the soft terms (both gravity- and anomaly-mediation) vanish. We enumerate subleading contributions and estimate their magnitude. We also describe model-independent physical implications of this scenario. These include the masses of anomalous and non-anomalous U(1)'s and the generic existence of a new hyperweak force under which leptons and/or quarks could be charged. We propose that such a gauge boson could be responsible for the ghost muon anomaly recently found at the Tevatron's CDF detector.Comment: 40 pages, 10 figure