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We study properties of moduli stabilization in the four dimensional N = 1 supergravity theory with heavy moduli and would-be saxion-axion multiplets including light string-theoretic axions. We give general formulation for the scenario that heavy moduli and saxions are stabilized while axions remain light, assuming that moduli are stabilized near the supersymmetric solution. One can find stable vacuum, i.e. non-tachyonic saxions, in the non-supersymmetric Minkowski vacua. We also discuss the cases, where the moduli are coupled to the supersymmetry breaking sector and/or moduli have contributions to supersymmetry breaking. We also study the models with axions originating from matter-like fields. Our analysis on moduli stabilization is applicable even if there are not light axion multiplets.
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We present a model of supersymmetry breaking in which the contributions from gravity/modulus, anomaly, and gauge mediation are all comparable. We term this scenario deflected mirage mediation, which is a generalization of the KKLT-motivated mirage mediation scenario to include gauge mediated contributions. These contributions deflect the gaugino mass unification scale and alter the pattern of soft parameters at low energies. In some cases, this results in a gluino LSP and light stops; in other regions of parameter space, the LSP can be a well-tempered neutralino. We demonstrate explicitly that competitive gauge-mediated terms can naturally appear within phenomenological models based on the KKLT setup by addressing the stabilization of the gauge singlet field which is responsible for the masses of the messenger fields. For viable stabilization mechanisms, the relation between the gauge and anomaly contributions is identical in most cases to that of deflected anomaly mediation, despite the presence of the Kahler modulus. Turning to TeV scale phenomenology, we analyze the renormalization group evolution of the supersymmetry breaking terms and the resulting low energy mass spectra. The approach sets the stage for studies of such mixed scenarios of supersymmetry breaking at the LHC.
In String Gas Cosmology, the simplest shape modulus fields are naturally stabilized by taking into account the presence of string winding and momentum modes. We determine the resulting effective potential for these fields and show that it obeys the de Sitter conjecture, one of the swampland criteria for effective field theories to be consistent with superstring theory.
Nonlinear supersymmetry is used to compute the general form of the effective D-brane action in type I string theory compactified to four dimensions in the presence of internal magnetic fields. In particular, the scalar potential receives three contributions: (1) a nonlinear part of the D-auxiliary component, associated to the Dirac-Born-Infeld action; (2) a Fayet-Iliopoulos (FI) D-term with a moduli-dependent coefficient; (3) a D-auxiliary independent (but moduli dependent) piece from the D-brane tension. Minimization of this potential leads to three general classes of vacua with moduli stabilization: (i) supersymmetric vacua allowing in general FI terms to be cancelled by non-trivial vacuum expectation values (VEVs) of charged scalar fields; (ii) anti-de Sitter vacua of broken supersymmetry in the presence of a non-critical dilaton potential that can be tuned at arbitrarily weak string coupling; (iii) if the dilaton is fixed in a supersymmetric way by three-form fluxes and in the absence of charged scalar VEVs, one obtains non supersymmetric vacua with positive vacuum energy.
We elaborate on integrable dynamical systems from scalar-gravity Lagrangians that include the leading dilaton tadpole potentials of broken supersymmetry. In the static Dudas-Mourad compactifications from ten to nine dimensions, which rest on these leading potentials, the string coupling and the space-time curvature become unbounded in some regions of the internal space. On the other hand, the string coupling remains bounded in several corresponding solutions of these integrable models. One can thus identify corrected potential shapes that could grant these features generically when supersymmetry is absent or non-linearly realized. On the other hand, large scalar curvatures remain present in all our examples. However, as in other contexts, the combined effects of the higher-derivative corrections of String Theory could tame them.
In the first part of this talk, a short overview of the ongoing debate on the existence of de Sitter vacua in string theory is presented. In the second part, the moduli stabilisation and inflation are discussed in the context of type IIB/F-theory. Considering a configuration of three intersecting $D7$ branes with fluxes, it is shown that higher loop effects inducing logarithmic corrections to the Kahler potential can stabilise the Kahler moduli in a de Sitter Vacuum. When a new Fayet-Iliopoulos term is included, it is also possible to generate the required number of e-foldings and satisfy the conditions for slow-roll inflation.
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