$F_4$ is the centralizer of $G_2$ inside an $E_8$. In other words, $E_8$ contains an $F_4\times G_2$ maximal subgroup. That's why by embedding the spin connection into the $E_8\times E_8$ heterotic gauge connection on $G_2$ holonomy manifolds, one obtains an $F_4$ gauge symmetry. See, for example,

http://arxiv.org/abs/hep-th/0108219

Gauge theories and string theory with $F_4$ gauge groups, e.g. in this paper

http://arxiv.org/abs/hep-th/9902186

depend on the fact that $F_4$ may be obtained from $E_6$ by a projection related to the nontrivial ${\mathbb Z}_2$ automorphism of $E_6$ which you may see as the left-right symmetry of the $E_6$ Dynkin diagram. This automorphism may be realized as a nontrivial monodromy which may break the initial $E_6$ gauge group to an $F_4$ as in

http://arxiv.org/abs/hep-th/9611119

Because of similar constructions, gauge groups including $F_4$ 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 $F_4/SO(9)$ coset (note that $F_4$ 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 $F_4/SO(9)$ fiber at each point:

http://motls.blogspot.com/2009/10/is-m-theory-hiding-cayley-plane-fibers.html

Less speculatively, the noncompact version $F_{4(4)}$ of the $F_4$ 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 $E_6/F_4$ type and some role is also being played by the fact that $F_4$ is the symmetry group of a $3\times 3$ 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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