F-theory from Fundamental Five-branes

TL;DR

This paper develops a worldvolume theory for a 6D gauge 2-form that embeds various string and M-theory frameworks, revealing new section conditions and a covariant reduction approach.

Contribution

It introduces a novel worldvolume formulation for F-theory with selfdual gauge fields, deriving new section conditions and unifying string and M-theory perspectives.

Findings

Re-derivation of the F-bracket from current algebra

Identification of a new section condition from Gauss's law

A covariant form for dimensional reduction of string coordinates

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 $X_{MN}(\sigma^P)$ 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 $\mathbf{10}$ of the GL(5) of the 5 $\sigma$'s (neglecting $\tau$). 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 Gau\ss{}'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.