F-theory with worldvolume sectioning

William D Linch,Warren Siegel

doi:10.1007/jhep04(2021)022

Abstract

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.

Highlights

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
The remainder of this note is organized as follows: in section 2 we review the 5-brane theory corresponding to the 3D type II string in a formulation amenable to generalization to 4D
The 3D string results from this description only after the dynamically-generated section conditions are imposed. (This is analogous to the reduction of the T-dual string to the usual string [8, 9].) We will re-derive these constraints in a language that is generalized to the 4D string, postponing the sectioning to the 3D string to section 5

Summary

Worldvolume action

We give a covariant 4D theory by an appropriate complexification of the 3D case in spinor notation. Interpreting X as the dynamical field, this means that in the Hamiltonian analysis of this system we should treat τ as the “time” parameter conjugate to the Hamiltonian In this sense, Y is not dynamical and we will gauge it to 0 presently. D10σ, where we have normalized the volume of the gauge-fixed σ direction to 1 Note that this expression for the Hamiltonian cannot be rewritten with manifest Spin(5, 5) invariance (e.g. Pαα → Pμ is a chiral ten-dimensional spinor). Generating a bosonic κ-symmetry; we use it to gauge Y → 0 After this is imposed, the field strengths can be written in manifestly Spin(5, 5)-covariant form μ := Fμ(+) = Pμ + (γm)μν ∂mXν andμ := Fμ(−) = Pμ − (γm)μν ∂mXν after combining SL(4; C) indices into the 16 × 16 Pauli matrices (γm)μν.

Algebras and backgrounds

Sectioning

Conclusions