Perturbative F-theory 10-brane and M-theory 5-brane

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 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, 5) duality symmetry is enlarged to the SO(6, 6) symmetry 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 are coset elements of SO(6, 6)/S0(6; C) which include 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.

Automated summary

The paper discusses the exceptional symmetry and U-duality theory in F-theory, examining the SO(5,5) U-duality symmetry acting on spacetime and worldvolume coordinates. The symmetry is enlarged in the Lagrangian formulation to SO(6,6), with proposed actions for F-theory 10-branes having both SO(5,5) and SO(6,6) symmetries. The gauge fields in the latter action include spacetime and worldvolume backgrounds, derived from SO(6,6)/S0(6;C) coset elements.