Symplectic structure in open string field theory III: Electric field

Abstract

We use a new formula for the symplectic structure on the phase space of open string field theory to evaluate the energy of a D-brane carrying a constant electric flux. This is shown to be consistent with the energy computed using the Dirac-Born-Infeld action through a generalization of the Ellwood invariant to nonpolynomial open string field theories.

Figures (12)

• Figure 4.1: The conformal maps $f^+$ (left) and $f^-$ (right) when $\lambda = 3$ and $q = 0.75$, shown together with the local coordinates for the Feynman diagram. They are characterized by conformally mapping the upper unit half-disk to the purple region on the UHP. The origin is mapped to the point $z = u_0$\ref{['eq:4.37anew']}.
• Figure 4.2: The local coordinates on the $\widetilde{w}_1$-frame when $\lambda = 3$. The black curve (i.e., the upper unit half-circle) is the contour for the zero mode integral \ref{['eq:4.4']} in the correlator \ref{['eq:4.34']}. It is orientated counter-clockwise due to the inversion and subsequent reparametrization.
• Figure 4.3: The position $u_0$ and mapping radius $\rho_0$ given in \ref{['eq:4.38new']}. They are plotted over the maximum extent of the lower Feynman region, see \ref{['eq:A.18']}. Observe $0< u_0 < u$ and $0 < \rho_0 < 1$.
• Figure 4.4: The nontrivial contributions to the symplectic form at third order $\Omega_3$ from \ref{['eq:4.41a']}, \ref{['eq:4.40']}, and \ref{['eq:4.41']} as a function of the stub parameter $\lambda$.
• Figure 4.5: The symplectic form at third order $\Omega_3$ as a function of the stub parameter $\lambda$. The red curve is the flow of $\Omega_3$ under the stub deformation with the initial condition fixed by $\lambda = 3$.