Aspects of F-Theory GUTs

The basic tools for model building in F-theory are reviewed and applied to the construction of SU(5) models. The flux mechanism for gauge symmetry breaking and doublet triplet splitting is analysed. A short account for the gauge coupling unification and the role of flux and Kaluza-Klein thresholds is also given.Comment: 37 pages. Based on Talk presented at Corfu 2011 Workshop "Fields and Strings: Theory - Cosmology - Phenomenology. September 14 - 18, 2011". (Prepared for the proceedings

On the Octonionic Self Duality equations of 3-brane Instantons

We study the octonionic selfduality equations for $p=3$-branes in the light cone gauge and we construct explicitly, instanton solutions for spherical and toroidal topologies in various flat spacetime dimensions $(D=5+1,7+1,8+1,9+1)$, extending previous results for $p=2$ membranes. Assuming factorization of time we reduce the self-duality equations to integrable systems and we determine explicitly periodic, in Euclidean time, solutions in terms of the elliptic functions. These solutions describe 4d associative and non-associative calibrations in $D=7,8$ dimensions. It turns out that for spherical topology the calibration is non compact while for the toroidal topology is compact. We discuss possible applications of our results to the problem of 3-brane topology change and its implications for a non-perturbative definition of the 3-brane interactions.Comment: 15 pages, 4 figure

Non-Minimal Quartic Inflation in Supersymmetric SO(10)

We describe how quartic ($\lambda \phi^4$) inflation with non-minimal coupling to gravity is realized in realistic supersymmetric $SO(10)$ models. In a well-motivated example the $16-\overline{16}$ Higgs multiplets, which break $SO(10)$ to $SU(5)$ and yield masses for the right-handed neutrinos, provide the inflaton field $\phi$. Thus, leptogenesis is a natural outcome in this class of $SO(10)$ models. Moreover, the adjoint (45-plet) Higgs also acquires a GUT scale value during inflation so that the monopole problem is evaded. The scalar spectral index $n_s$ is in good agreement with the observations and $r$, the tensor to scalar ratio, is predicted for realistic values of GUT parameters to be of order $10^{-3}-10^{-2}$.Comment: 10 pages, 1 figur