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Register a new userDynamically sequestered F-term uplifting in extra dimension
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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 Minkowski minimum where the radius modulus is stabilized, while gaugino masses would be a mirage type.
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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 Kahler 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 ORaifeartaigh 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 those in the KKLT scenario. One of the quantitative changes, which are relevant to the phenomenology, is a larger hierarchy between the modulus mass m_T and the gravitino mass $m_{3/2}$, i.e., $m_T/m_{3/2} = {cal O}(a^2)$, where $a sim 4 pi^2$. In spite of such a large mass, the modulus F-term is suppressed not like $F^T = {cal O}(m_{3/2}/a^2)$, but like $F^T = {cal O}(m_{3/2}/a)$ for $ln (M_{Pl}/m_{3/2}) sim a$, because of an enhancement factor coming from the X-T mixing. Then we typically find a mirage-mediation pattern of gaugino masses of ${cal O}(m_{3/2}/a)$, while the scalar masses would be generically of ${cal O}(m_{3/2})$.
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.
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 with small vacuum energy and large gravitino mass can be found even for very small values of W_0. Models where D-terms are allowed to vanish at finite vevs of moduli fields - denoted `cancellable D-terms - and the ones where D-terms may vanish only at infinite vevs of some moduli - denoted `non-cancellable - differ markedly in their properties. It turns out that the tuning with respect to the Planck scale required in the case of cancellable D-terms is much weaker than in the case of non-cancellable ones. We have shown that, against intuition, a vanishing D-term can trigger F-term uplifting of the vacuum energy due to the stringent constraint it imposes on vacuum expectation values of charged fields. Finally we note that our models only rely on two dimensionful parameters: M_P and W_0.
In this talk we present the result for the $n_f$ dependent piece of the three-loop cusp anomalous dimension in QCD. Remarkably, it is parametrized by the same simple functions appearing in analogous anomalous dimensions in ${mathcal N}=4$ SYM at one and two loops. We also compute all required master integrals using a recently proposed refinement of the differential equation method. The analytic results are expressed in terms of harmonic polylogarithms of uniform weight.
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 numbers of the Calabi-Yau manifold. We analyse this case in detail and show that once the metastability condition is satisfied it is possible to reconstruct in a systematic way the local form of the superpotential that is needed to stabilise all the fields. We apply then this procedure to construct some examples of models where the superpotential takes a realistic form allowed by flux backgrounds and gaugino condensation effects, for which a viable vacuum arises without the need of invoking corrections to the Kahler potential breaking the no-scale property or uplifting terms. We finally discuss the prospects of constructing potentially realistic models along these lines.
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