Rolling Tachyon with Electric and Magnetic Fields -- T-duality approach -----

TL;DR

The work analyzes rolling tachyon decay on unstable D$p$-branes in the presence of constant world-volume electric and magnetic fields. It introduces a systematic chain of Lorentz boosts, rotations, and T-duality to construct the D$p$-brane boundary state with background gauge fields, revealing how electric and magnetic fields modify couplings to closed-string states and the decay time-scale via the Born–Infeld factor and Lorentz dilation. A detailed examination of couplings shows that electric fields enhance interactions with higher massive closed-string modes along the field direction and slow the decay, while magnetic fields add transverse structure and induce additional D-brane density; the results are corroborated by an effective DBI-type field theory. Overall, the paper clarifies the interplay between rolling tachyon dynamics, background gauge fields, and open/closed string couplings, providing a coherent boundary-state and EFT picture of D-brane decay in flux backgrounds.

Abstract

We study the decay of unstable D$p$-branes when the world-volume gauge field is turned on. We obtain the relevant Dp-brane boundary state with electric and magnetic fields by boosting and rotating the rolling tachyon boundary state of a D(p-1)-brane and then T-dualizing along one of the transverse directions. A simple recipe to turn on the gauge fields in the boundary state is given. We find that the effect of the electric field is to parametrically enhance coupling of closed string oscillation modes along the electric field direction and provide an intuitive understanding of the result in the T-dualized picture. We also analyze the system by using the effective field theory and compare the result with the boundary state approach.

Figures (3)

• Figure 1: Behavior of $\rho_{\rm tachyon} = \rho_{\rm dilaton} =-T_{ii} (i \ne 0,1)$ (vertical axis in arbitrary unit) in $y^0 = [0, 10]$ and $\widetilde{\lambda} = [0, 1/2]$ parameter space. The left is for $e=0$, while the right is for $e=0.9$.
• Figure 2: Behavior of $T_{11}$ (vertical axis in arbitrary unit) in $y^0 = [0, 10]$ and $\widetilde{\lambda} = [0, 1/2]$ parameter space. The left is for $e=0$, while the right is for $e=0.9$.
• Figure 3: Behavior of $h_2$ (vertical axis in arbitrary unit) in $y^0 = [0, 10]$ and $\widetilde{\lambda} = [0, 1/2]$ parameter space. The left is for $e=0$, while the right is for $e=0.9$.