Gauge Transformation of Double Field Theory for Open String

Chen-Te Ma

Published 2014-11-02Version 1

I combine the symmetry structure of both the normal and transverse coordinates to construct the Dirac-Born-Infeld (DBI) theory. Normal coordinates are dual to Neumann boundary conditions and transverse coordinates dual to Dirichlet boundary conditions. The gauge transformation of the generalized metric is also governed by the generalized Lie derivative as the massless closed string field theory. The massless closed string field theory gives $C$-bracket, but the DBI theory gives the $F$-bracket from the closed algebra. The $F$-bracket can be a $\alpha^{\prime}$ deformation of the $C$-bracket. From the symmetry, we can deduce the suitable action with non-zero flux in open string. From the equations of motion of the scalar dilaton, it offers the generalized scalar curvature. Finally, I show the classical equivalence between the double sigma model and normal sigma model for open string.