Zygmunt Lalak

Hierarchical supersymmetry breaking and dynamical determination of compactification parameters by non-perturbative effects

The characteristics of the effective potentials coming from phenomenologically promising compactified superstring theories are examined, paying special attention to the supersymmetry breaking issue. We find a mechanism for generating the large gauge hierarchy by gaugino condensation effect in the case that the hidden sector possesses more than one condensate. We construct an explicit example based on orbifold compactification in which this is realized. Minimization of the effective potential not only determines the gauge hierarchy but also fixes other important parameters of the theory, in particular the gauge coupling constant at the unification point and the expectation values of the moduli which give the size and shape of the compactified space. These get reasonable values which may, in turn, lead to a determination of the family mass hierarchy.

Strongly Coupled Perturbations in Two-Field Inflationary Models

We study models of inflation with two scalar fields and non-canonical kinetic terms, focusing on the case in which the curvature and isocurvature perturbations are strongly coupled to each other. In the regime where a heavy mode can be identified and integrated out, we clarify the passage from the full two-field model to an effectively single-field description. However, the strong coupling sets a new scale in the system, and affects the evolution of the perturbations as well as the beginning of the regime of validity of the effective field theory. In particular, the predictions of the model are sensitive to the relative hierarchy between the coupling and the mass of the heavy mode. As a result, observables are not given unambiguously in terms of the parameters of an effectively single field model with non-trivial sound speed. Finally, the requirement that the sound horizon crossing occurs within the regime of validity of the effective theory leads to a lower bound on the sound speed. Our analysis is done in an extremely simple toy model of slow-roll inflation, which is chosen for its tractability, but is non-trivial enough to illustrate the richness of the dynamics in non-canonical multi-field models.

Racetrack inflation and assisted moduli stabilisation

We present a model of inflation based on a racetrack model without flux stabilization. The initial conditions are set automatically through topological inflation. This ensures that the dilaton is not swept to weak coupling through either thermal effects or fast roll. Including the effect of non-dilaton fields we find that moduli provide natural candidates for the inflaton. The resulting potential generates slow-roll inflation without the need to fine-tune parameters. The energy scale of inflation must be near the GUT scale and the scalar density perturbation generated has a spectrum consistent with WMAP data.

Gaugino condensation, moduli potential and supersymmetry breaking in M theory models

Abstract We derive the explicit form, and discuss some properties of the moduli-dependent effective potential arising from M-theory compactified on M 4 × X × S 1 / Z 2 , when one of the boundaries supports a strongly interacting gauge sector and induces gaugino condensation. We discuss the relation between the explicit gaugino condensate and effective superpotential formulations and find interesting differences with respect to the situation known from the weakly coupled heterotic string case. The moduli dependence of the effective potential turns out to be more complicated than expected, and perhaps offers new clues to the stabilization problem.

Five-dimensional aspects of M theory dynamics and supersymmetry breaking

We discuss the reduction of the eleven-dimensional M-theory effective Lagrangian, considering first compactification from eleven to five dimensions on a Calabi-Yau manifold, followed by reduction to four dimensions on an S1/Z2 line segment at a larger distance scale. The Calabi-Yau geometry leads to a structure of the five-dimensional Lagrangian that has more freedom than the eleven-dimensional theory. In five dimensions one obtains a non-linear σ model coupled to gravity, which implies non-trivial dynamics for the scalar moduli fields in the bulk of the Z2 orbifold. We discuss solutions to the five-dimensional equations of motion in the presence of sources localized on the boundaries of the Z2 orbifold that may trigger supersymmetry breaking, e.g., gaugino condensates. The transmission of supersymmetry breaking from the hidden wall to the visible wall is demonstrated in specific models. The role of the messenger of supersymmetry breaking may be played by the gravity supermultiplet and/or by scalar hypermultiplets. The latter include the universal hypermultiplet associated with the Calabi-Yau volume, and also the hypermultiplets associated with deformations of its complex structure, which mix in general.

Higher-order scalar interactions and SM vacuum stability

A bstractInvestigation of the structure of the Standard Model effective potential at very large field strengths opens a window towards new phenomena and can reveal properties of the UV completion of the SM. The map of the lifetimes of the vacua of the SM enhanced by nonrenormalizable scalar couplings has been compiled to show how new interactions modify stability of the electroweak vacuum. Whereas it is possible to stabilize the SM by adding Planck scale suppressed interactions and taking into account running of the new couplings, the generic effect is shortening the lifetime and hence further destabilisation of the SM electroweak vacuum. These findings have been illustrated with phase diagrams of modified SM-like models. It has been demonstrated that stabilisation can be achieved by lowering the suppression scale of higher order operators while picking up such combinations of new couplings, which do not deepen the new minima of the potential. Our results show the dependence of the lifetime of the electroweak minimum on the magnitude of the new couplings, including cases with very small couplings (which means very large effective suppression scale) and couplings vastly different in magnitude (which corresponds to two different suppression scales).

Universal constraints on low-energy flavour models

A bstractIt is pointed out that in a general class of flavour models one can identify certain universally present FCNC operators, induced by the exchange of heavy flavour messengers. Their coefficients depend on the rotation angles that connect flavour and fermion mass basis. The lower bounds on the messenger scale are derived using updated experimental constraints on the FCNC operators. The obtained bounds are different for different operators and in addition they depend on the chosen set of rotations. Given the sensitivity expected in the forthcoming experiments, the present analysis suggests interesting room for discovering new physics. As the highlights emerge the leptonic processes, μ → eγ, μ → eee and μ → e conversion in nuclei.

Beyond MFV in family symmetry theories of fermion masses

Minimal Flavour Violation (MFV) postulates that the only source of flavour changing neutral currents and CP violation, as in the Standard Model, is the CKM matrix. However it does not address the origin of fermion masses and mixing and models that do usually have a structure that goes well beyond the MFV framework. In this paper we compare the MFV predictions with those obtained in models based on spontaneously broken (horizontal) family symmetries, both Abelian and non-Abelian. The generic suppression of flavour changing processes in these models turns out to be weaker than in the MFV hypothesis. Despite this, in the supersymmetric case, the suppression may still be consistent with a solution to the hierarchy problem, with masses of superpartners below 1 TeV. A comparison of FCNC and CP violation in processes involving a variety of different family quantum numbers should be able to distinguish between various family symmetry models and models satisfying the MFV hypothesis.

Four-Dimensional Supergravities from Five-Dimensional Brane Worlds

We give the explicit form of the four-dimensional effective supergravity action, which describes low-energy physics of the Randall–Sundrum model with moduli fields in the bulk and charged chiral matter living on the branes. The relation between 5d and 4d physics is explicit: the low-energy action is derived from the compactification of a locally supersymmetric model in five dimensions. The presence of odd Z2 parity scalars in the bulk gives rise to effective potential for the radion in four dimensions. We describe the mechanism of supersymmetry breaking mediation, which relies on non-trivial configuration of these Z2-odd bulk fields. Broken supersymmetry leads to stabilization of the interbrane distance.

Beyond the standard embedding in M-theory on S1/Z2

In this paper we discuss compactifications of M-theory to four dimensions on X × S1/Z2, in which non-standard embeddings in the E8 × E8 vacuum gauge bundle are considered. At the level of the effective field theory description of Horava and Witten, this provides a natural extension of well known results at weak coupling, to strongly coupled E8 × E8 heterotic strings. As an application of our results, we discuss models which exhibit an anomalous U(1)A symmetry in four dimensions, and show how this emerges from the reduction of the d = 11 topological term C ∧ G ∧ G, and how it is consistent with d = 4 anomaly cancellation in M-theory. As a further application of non-standard embeddings, we show how it is possible to obtain an inverse hierarchy of gauge couplings, where the observable sector is more strongly coupled than the hidden one. The basic construction and phenomenological viability of these scenarios is demonstrated.