T-dual superstring Lagrangian with double zweibeins

Abstract

We present superstring Lagrangians with manifest T-duality. The Lagrangian version of the section conditions are necessary to make Lagrangians to be general coordinate invariant. We show the general solution of section conditions. The D-dimensional left and right moving currents are the 2D-dimensional chiral current which causes the chiral boson problem. We solve the problem by adding the unphysical 2D-dimensional anti-selfdual current with the selfduality constraints. The

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

“…It contains winding modes even in an uncompactified space, and the D-dimensional space includes time direction to describe dynamical gravity. All string modes including massive modes are described in the T-theory which has been developed [1][2][3][4][5][6][7][8][9][10][11]. Section conditions eliminate winding modes while the string field theory condition L 0 = L0 mixes massive winding modes with massive oscillator states [12].…”

“…This SO(5, 5) current algebra is recognized as the F-theory 10brane current algebra by doubling the worldvolume coordinate as shown in (3.21), (3.24) and (3.25). In subsection 4.1 we begin by reviewing the double zweibein method to obtain the worldsheet covariant action [10,11] as a method to overcome the chiral action [53]. By applying this method to F-theory we obtain the SO(5, 5) F-theory 10-brane action in the Hamiltonian formalism in subsection 4.2.…”

“…In order to construct the worldvolume covariant Lagrangian we include the ones for the anti-selfdual currents. At first, we review how to construct the worldsheet covariant action by using the double zweibein method [10,11]. Then we propose actions for the F10-brane with both the SO(5, 5) symmetric Hamiltonian formulation and the SO(6, 6) symmetric Lagrangian formulation.…”

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

“…It contains winding modes even in an uncompactified space, and the D-dimensional space includes time direction to describe dynamical gravity. All string modes including massive modes are described by T-theory which has been developped [1][2][3][4][5][6][7][8][9][10][11]. Section conditions eliminate winding modes while the string field theory condition L 0 = L0 mixes massive winding modes with massive oscillator states [12].…”

“…This SO(5,5) current algebra is recognized as the F-theory 10-brane current algebra by doubling the worldvolume coordinate as shown in (3.20), (3.23) and (3.24). In subsection 3.1 we begin by reviewing the double zweibein method to obtain the worldsheet covariant action [10,11] as a method to overcome the chiral action [53]. By applying this method to F-theory we obtain the SO(5,5) F-theory 10-brane action in the Hamiltonian formalism in subsection 3.2.…”