  The exceptional symmetry is realized perturbatively in F-theory which is the
manifest U-duality theory. The SO(5,5) U-duality symmetry acts on both the 16
spacetime coordinates and the 10 worldvolume coordinates. Closure of the
Virasoro algebra requires the Gauss law constraints on the worldvolume. This
set of current algebras describes a F-theory 10-brane. The SO(5,5) duality
symmetry is enlarged to the SO(6,6) in the Lagrangian formulation. We propose
actions of the F-theory 10-brane with SO(5,5) and SO(6,6) symmetries. The gauge
fields of the latter action is coset elements of SO(6,6)/SO(6;C) which includes
both the SO(5,5)/SO(5;C) spacetime backgrounds and the worldvolume backgrounds.
The SO(5,5) current algebra obtained from the Pasti-Sorokin-Tonin M5-brane
Lagrangian leads to the theory behind M-theory, namely F-theory. We also
propose an action of the perturbative M-theory 5-brane obtained by sectioning
the worldvolume of the F-theory 10-brane.
