We study the cosmology of a recent model of supersymmetry breaking, in the presence of a tuneable positive cosmological constant, based on a gauged shift symmetry of a string modulus that can be identified with the string dilaton. The minimal spectru
m of the `hidden supersymmetry breaking sector consists then of a vector multiplet that gauges the shift symmetry of the dilaton multiplet and when coupled to the MSSM leads to a distinct low energy phenomenology depending on one parameter. Here we study the question if this model can also lead to inflation by identifying the dilaton with the inflaton. We find that this is possible if the Kahler potential is modified by a term that has the form of NS5-brane instantons, leading to an appropriate inflationary plateau around the maximum of the scalar potential, depending on two extra parameters. This model is consistent with present cosmological observations without modifying the low energy particle phenomenology associated to the minimum of the scalar potential.
We consider a class of models with gauged U(1)_R symmetry in 4D N=1 supergravity that have, at the classical level, a metastable ground state, an infinitesimally small (tunable) positive cosmological constant and a TeV gravitino mass. We analyse if t
hese properties are maintained under the addition of visible sector (MSSM-like) and hidden sector state(s), where the latter may be needed for quantum consistency. We then discuss the anomaly cancellation conditions in supergravity as derived by Freedman, Elvang and Kors and apply their results to the special case of a U(1)_R symmetry, in the presence of the Fayet-Iliopoulos term ($xi$) and Green-Schwarz mechanism(s). We investigate the relation of these anomaly cancellation conditions to the naive field theory approach in global SUSY, in which case U(1)_R cannot even be gauged. We show the two approaches give similar conditions. Their induced constraints at the phenomenological level, on the above models, remain strong even if one lifted the GUT-like conditions for the MSSM gauge couplings. In an anomaly-free model, a tunable, TeV-scale gravitino mass may remain possible provided that the U(1)_R charges of additional hidden sector fermions (constrained by the cubic anomaly alone) do not conflict with the related values of U(1)_R charges of their scalar superpartners, constrained by existence of a stable ground state. This issue may be bypassed by tuning instead the coefficients of the Kahler connection anomalies (b_K, b_{CK}).
In MSSM models with various boundary conditions for the soft breaking terms (m_{soft}) and for a higgs mass of 126 GeV, there is a (minimal) electroweak fine-tuning Deltaapprox 800 to 1000 for the constrained MSSM and Deltaapprox 500 for non-universa
l gaugino masses. These values, often regarded as unacceptably large, may indicate a problem of supersymmetry (SUSY) breaking, rather than of SUSY itself. A minimal modification of these models is to lower the SUSY breaking scale in the hidden sector (sqrt f) to few TeV, which we show to restore naturalness to more acceptable levels Deltaapprox 80 for the most conservative case of low tan_beta and ultraviolet boundary conditions as in the constrained MSSM. This is done without introducing additional fields in the visible sector, unlike other models that attempt to reduce Delta. In the present case Delta is reduced due to additional (effective) quartic higgs couplings proportional to the ratio m_{soft}/(sqrt f) of the visible to the hidden sector SUSY breaking scales. These couplings are generated by the auxiliary component of the goldstino superfield. The model is discussed in the limit its sgoldstino component is integrated out so this superfield is realized non-linearly (hence the name of the model) while the other MSSM superfields are in their linear realization. By increasing the hidden sector scale sqrt f one obtains a continuous transition for fine-tuning values, from this model to the usual (gravity mediated) MSSM-like models.
In this note we study the constraints on F-theory GUTs with extra $U(1)$s in the context of elliptic fibrations with rational sections. We consider the simplest case of one abelian factor (Mordell-Weil rank one) and investigate the conditions that ar
e induced on the coefficients of its Tate form. Converting the equation representing the generic hypersurface $P_{112}$ to this Tates form we find that the presence of a U(1), already in this local description, is consistent with the exceptional ${cal E}_6$ and ${cal E}_7$ non-abelian singularities. We briefly comment on a viable ${cal E}_6times U(1)$ effective F-theory model.
We construct a supergravity model whose scalar degrees of freedom arise from a chiral superfield and are solely a scalaron and an axion that is very heavy during the inflationary phase. The model includes a second chiral superfield $X$, which is subj
ect however to the constraint $X^2=0$ so that it describes only a Volkov - Akulov goldstino and an auxiliary field. We also construct the dual higher - derivative model, which rests on a chiral scalar curvature superfield ${cal R}$ subject to the constraint ${cal R}^2=0$, where the goldstino dual arises from the gauge - invariant gravitino field strength as $gamma^{mn} {cal D}_m psi_n$. The final bosonic action is an $R+R^2$ theory involving an axial vector $A_m$ that only propagates a physical pseudoscalar mode.
Experimental data on the neutrino mixing and masses strongly suggest an underlying approximate symmetry of the relevant Yukawa superpotential terms. Intensive phenomenological explorations during the last decade indicate that permutation symmetries s
uch as S_4, A_4 and their subgroups, under certain assumptions and vacuum alignments, predict neutrino mass textures compatible with such data. Motivated by these findings, in the present work we analyse the neutrino properties in F-theory GUT models derived in the framework of the maximal underlying E_8 symmetry in the elliptic fibration. More specifically, we consider local F-SU(5) GUT models and study in detail spectral cover geometries with monodromies associated to the finite symmetries S_4, A_4 and their transitive subgroups, including the dihedral group D_4 and Z_2 X Z_2. We discuss various issues that emerge in the implementation of S_4, A_4 neutrino models in the F-theory context and suggest how these can be resolved. Realistic models are presented for the case of monodromies based on their transitive subgroups. We exemplify this procedure with a detailed analysis performed for the case of Z_2 X Z_2 model.
A worldsheet realization of the refined topological string is proposed in terms of physical string amplitudes that compute generalized N=2 F-terms of the form F_{g,n} W^{2g}Y^{2n} in the effective supergravity action. These terms involve the chiral W
eyl superfield W and a superfield Y defined as an N=2 chiral projection of a particular anti-chiral T-bar vector multiplet. In Heterotic and Type I theories, obtained upon compactification on the six-dimensional manifold K3xT2, T is the usual Kahler modulus of the T2 torus. These amplitudes are computed exactly at the one-loop level in string theory. They are shown to reproduce the correct perturbative part of the Nekrasov partition function in the field theory limit when expanded around an SU(2) enhancement point of the string moduli space. The two deformation parameters epsilon_- and epsilon_+ of the Omega-supergravity background are then identified with the constant field-strength backgrounds for the anti-self-dual graviphoton and self-dual gauge field of the T-bar vector multiplet, respectively.
For a 4D N=1 supersymmetric model with a low SUSY breaking scale (f) and general Kahler potential K(Phi^i,Phi_j^*) and superpotential W(Phi^i) we study, in an effective theory approach, the relation of the goldstino superfield to the (Ferrara-Zumino)
superconformal symmetry breaking chiral superfield X. In the presence of more sources of supersymmetry breaking, we verify the conjecture that the goldstino superfield is the (infrared) limit of X for zero-momentum and Lambda->infty. (Lambda is the effective cut-off scale). We then study the constraint X^2=0, which in the one-field case is known to decouple a massive sgoldstino and thus provide an effective superfield description of the Akulov-Volkov action for the goldstino. In the presence of additional fields that contribute to SUSY breaking we identify conditions for which X^2=0 remains valid, in the effective theory below a large but finite sgoldstino mass. The conditions ensure that the effective expansion (in 1/Lambda) of the initial Lagrangian is not in conflict with the decoupling limit of the sgoldstino (1/m_sgoldstinosim Lambda/f, f<Lambda^2).
We revisit local F-theory SO(10) and SU(5) GUTs and analyze their properties within the framework of the maximal underlying E_8 symmetry in the elliptic fibration. We consider the symmetry enhancements along the intersections of seven-branes with the
GUT surface and study in detail the embedding of the abelian factors undergoing monodromies in the covering gauge groups. We combine flux data from the successive breaking of SO(10) to SU(5) gauge symmetry and subsequently to the Standard Model one, and further constrain the parameters determining the models particle spectra. In order to eliminate dangerous baryon number violating operators we propose ways to construct matter parity like symmetries from intrinsic geometric origin. We study implementations of the resulting constrained scenario in specific examples obtained for a variety of monodromies.
This proceeding is based on arXiv:1105.0591 [hep-th] where we consider breaking of supersymmetry in intersecting D-brane configurations by slight deviation of the angles from their supersymmetric values. We compute the masses generated by radiative c
orrections for the adjoint scalars on the brane world-volumes. In the open string channel, the string two-point function receives contributions only from the infrared limits of N~4 and N~2 supersymmetric configurations, via messengers and their Kaluza-Klein excitations, and leads at leading order to tachyonic directions.
