F-theory from fundamental five-branes

William D Linch,Warren Siegel

doi:10.1007/jhep02(2021)047

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.

Highlights

Our treatment of fundamental branes differs from previous versions [20,21,22,23,24,25,26] in that the worldvolume fields XMN describing spacetime coordinates are gauge fields
We describe the worldvolume for the bosonic sector of the lower-dimensional Ftheory that embeds 4D, N=1 M-theory and the 3D Type II superstring
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

Summary

Currents and constraints

Covariant selfdual 6D field theory has been described previously in terms of an action [27]. The selfdual field strengths are the currents for the covariant derivatives [28]. The Virasoro algebra is defined by the energymomentum tensor for the selfdual field strength. Various section-like conditions can be introduced by replacing some string coordinates in these constraints with their zero-modes [29]: Virasoro dimensional reduction section condition. 2. We treat Gauß’s law Um, which arises because the 6D X is a gauge field, as a dimensional reduction condition since it’s linear in the string variables. We have a new covariant dimensional reduction condition. Since ∂[m∂n] = 0, both dimensional reduction conditions can be written with P replaced with either or : the latter allows them to commute with Virasoro.) It replaces PL − PR used in the manifestly T-dual version of the string that has doubled coordinates. The section conditions include S, originally found by closure of gauge transformations (see below) in F-gravity [9], and a new one U that mutually restricts x and σ.

Algebras and gauge symmetries

Backgrounds

Conclusions