F-theory from fundamental five-branes

Abstract

Abstract We describe the worldvolume for the bosonic sector of the lower-dimensional F-theory that embeds 4D, N=1 M-theory and the 3D Type II superstring. The worldvolume (5-brane) theory is that of a single 6D gauge 2-form XMN(σP) whose field strength is selfdual. Thus unlike string theory, the spacetime indices are tied to the worldsheet ones: in the Hamiltonian formalism, the spacetime coordinates are a 10 of the GL(5) of the 5 σ’s (neglecting τ). The current algebra gives a rederivation of the F-bracket. The background-independent subalgebra of the Virasoro algebra gives the usual section condition, while a new type of section condition follows from Gauß’s law, tying the worldvolume to spacetime: solving just the old condition yields M-theory, while solving only the new one gives the manifestly T-dual version of the string, and the combination produces the usual string. We also find a covariant form of the condition that dimensionally reduces the string coordinates.