F4 is the centralizer of G2 inside an E8. In other words, E8 contains an F4×G2 maximal subgroup. That's why by embedding the spin connection into the E8×E8 heterotic gauge connection on G2 holonomy manifolds, one obtains an F4 gauge symmetry. See, for example,
http://arxiv.org/abs/hep-th/0108219
Gauge theories and string theory with F4 gauge groups, e.g. in this paper
http://arxiv.org/abs/hep-th/9902186
depend on the fact that F4 may be obtained from E6 by a projection related to the nontrivial Z2 automorphism of E6 which you may see as the left-right symmetry of the E6 Dynkin diagram. This automorphism may be realized as a nontrivial monodromy which may break the initial E6 gauge group to an F4 as in
http://arxiv.org/abs/hep-th/9611119
Because of similar constructions, gauge groups including F4 factors (sometimes many of them) are common in F-theory:
http://arxiv.org/abs/hep-th/9701129
More speculatively (and outside established string theory), a decade ago, Pierre Ramond had a dream
http://arxiv.org/abs/hep-th/0112261
http://arxiv.org/abs/hep-th/0301050
that the 16-dimensional Cayley plane, the F4/SO(9) coset (note that F4 may be built from SO(9) by adding a 16-spinor of generators), may be used to define all of M-theory. As far as I can say, it hasn't quite worked but it is interesting. Sati and others recently conjectured that M-theory may be formulated as having a secret F4/SO(9) fiber at each point:
http://motls.blogspot.com/2009/10/is-m-theory-hiding-cayley-plane-fibers.html
Less speculatively, the noncompact version F4(4) of the F4 exceptional group is also the isometry of a quaternion manifold relevant for the maximal N=2 matter-Einstein supergravity, see
http://arxiv.org/abs/hep-th/9708025
In that paper, you may also find cosets of the E6/F4 type and some role is also being played by the fact that F4 is the symmetry group of a 3×3 matrix Jordan algebra of octonions.
A very slight extension of this answer is here:
http://motls.blogspot.com/2011/10/any-use-for-f4-in-hep-th.html
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