  F-theory is a non-perturbative formulation of type IIB superstring theory
which allows for the decoupling of gravity and for the formulation of GUT
theories based on the gauge group E6. In this paper we explore F-theory models
in which the low energy supersymmetric theory contains the particle content of
three 27 dimensional representations of the underlying E6 gauge group, plus two
extra right-handed neutrinos predicted from F and D flatness. The resulting TeV
scale effective theory resembles either the E6SSM or the NMSSM+, depending on
whether an additional Abelian gauge group does or does not survive. However
there are novel features compared to both these models as follows: (i) If the
additional Abelian gauge group is unbroken then it can have a weaker gauge
coupling than in the E6SSM; (ii) If the additional Abelian gauge group is
broken then non-perturbative effects can violate the scale invariance of the
NMSSM+ leading to a generalised model; (iii) Unification is achieved not at the
field theory level but at the F-theory level since the gauge couplings are
split by flux effects, negating the need for any additional doublet states
which are usually required; (iv) Proton decay is suppressed by the geometric
coupling suppression of a singlet state, a mechanism peculiar to F-theory,
which effectively suppresses the coupling of the exotic charge -1/3 colour
triplet state D to quarks and leptons; (v) The D bar couples to left-handed
leptoquarks, providing characteristic and striking signatures at the LHC.
