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A bstract We include in F-theory, through open Type I F-theory branes (F-branes), string theories with N = 1 supersymmetry, both Type I and heterotic. Type I branes are distinguished from Type II by worldvolume parity projection. The same open Type I branes describe both open Type I superstrings and closed heterotic upon different sectionings from F-branes to worldsheets, while closed Type I superstrings arise from closed Type I branes. (Type II superstrings come from closed Type II branes, as described previously.) F-theory manifests the exceptional-group U-duality symmetry, with all massless bosonic fields in a single gauge coset. This coset branches to the usual bosonic supergravity fields upon sectioning. We examine in detail the simple case of D = 3 F-theory: parity projection reduces the Type II coset SL(5)/SO(3,2) to the Type I coset SO(3,3)/SO(2,1) 2 = SL(4)/SO(2,2). 

A bstract The exceptional symmetry is realized perturbatively in F-theory which is the manifest U-duality theory. The SO(5) U-duality symmetry acts on both the 16 space-time 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) duality symmetry is enlarged to the SO(6) symmetry in the Lagrangian formulation. We propose actions of the F-theory 10-brane with SO(5) and SO(6) symmetries. The gauge fields of the latter action are coset elements of SO(6)/SO(6; ℂ) which include both the SO(5)/SO(5; ℂ) spacetime backgrounds and the worldvolume backgrounds. The SO(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. 

A bstract We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 5D, N=1 M-theory and the 4D type II superstring. This theory is a complexification of the fundamental 5-brane theory that embeds the 4D, N=1 M-theory of the 3D type II string in a sense that we make explicit at the level of the Lagrangian and Hamiltonian formulations. We find three types of section condition: in spacetime, on the worldvolume, and one tying them together. The 5-brane theory is recovered from the new theory by a double dimensional reduction.