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In this paper we consider a set of soft supersymmetry breaking terms within the NMSSM which leads to a small hierarchy between the supersymmetry breaking scale and the electroweak scale. Specifically only the gaugino masses and the soft term in the Higgs sector are non-vanishing at the GUT scale. This pattern can be found in gaugino mediated models and in higher-dimensional orbifold GUTs. We study the phenomenology of this scenario and find different low energy spectra depending on the Yukawa coupling $\lambda$ of the NMSSM singlet. In particular, for low values of $\lambda$ the singlet is the lightest scalar and the singlino is the LSP while for large values of $\lambda$ both are heavy and the gravitino can be the LSP. The singlet pseudoscalar is very light in the entire parameter space., Comment: Latex, 21+1 pages, 5 figures; v2: References and comments added

Models of 4D $\mathcal{N}=1$ supergravity coupled to chiral multiplets with vanishing or positive scalar potential have been denoted as no-scale. Of particular interest in the context of string theory are models which additionally possess a shift-symmetry. In this case there exists a dual description of chiral models in terms of real linear multiplets. We classify all ungauged shift-symmetric no-scale supergravities in both formulations and verify that they match upon dualization. Additionally, we comment on the realizations within effective supergravities descending from string compactifications., Comment: 31 pages; v2: References added

We study a model of inflation with terms quadratic and logarithmic in the Ricci scalar, where the gravitational action is $f(R)=R+\alpha R^2+\beta R^2 \ln R$. These terms are expected to arise from one loop corrections involving matter fields in curved space-time. The spectral index $n_s$ and the tensor to scalar ratio yield $10^{-4}\lesssim r\lesssim0.03$ and $0.94\lesssim n_s \lesssim 0.99$. i.e. $r$ is an order of magnitude bigger or smaller than the original Starobinsky model which predicted $r\sim 10^{-3}$. Further enhancement of $r$ gives a scale invariant $n_s\sim 1$ or higher. Other inflationary observables are $d n_s/d\ln k \gtrsim -5.2 \times 10^{-4},\, \mu \lesssim 2.1 \times 10^{-8} ,\, y \lesssim 2.6 \times 10^{-9}$. Despite the enhancement in $r$, if the recent BICEP2 measurement stands, this model is disfavoured., Comment: LaTeX, 9+1 pages, 5 figures

In this letter we study the Higgs mass in the NMSSM with supersymmetry breaking at high scales $M_{SS}$. With the Standard Model as the effective low energy theory, the computation of the Higgs mass relies on the matching condition of the quartic coupling $\lambda$ at $M_{SS}$. In the MSSM, the latter is fixed to a semi-positive value and, thus, sets an upper bound on the SUSY-breaking scale near $M_{SS}\simeq 10^{10}\text{GeV}$. In the NMSSM, $\lambda(M_{SS})$ receives an additional contribution induced by the singlet which allows for negative values of $\lambda(M_{SS})$. In turn, for the measured value of the Higgs mass we find that $M_{SS}$ can take any value up to the GUT scale. Furthermore, the choice of universal soft terms favors SUSY-breaking scales close to the GUT scale., Comment: 14 pages, 5 figures