Decay of Unstable D-branes with Electric Field

TL;DR

This work analyzes the decay of unstable D-branes in the presence of a constant electric field by combining target-space open-string EFT methods with a BCFT framework. The authors show that the rolling tachyon couples to the background flux to yield a two-component late-time behavior: a uniform fundamental-string density along the electric field and a rolling tachyon sector whose evolution is slowed by the field-induced time-dilation, with explicit expressions for the energy-momentum tensor and string charge sources. They construct the exact marginal deformation in BCFT, build the corresponding boundary state in a suitably compactified setup, and extract massless closed-string sources that agree with the target-space results; in certain limits the boundary state exhibits divergences at higher levels, providing insight into the structure of the decay process. The analysis is extended to superstrings and connected to a DBI-type EFT that reproduces the late-time source behavior and RR couplings, highlighting the role of the open-string metric and boundary states in tachyon condensation with electric flux.

Abstract

Using the techniques of two dimensional conformal field theory we construct time dependent classical solutions in open string theory describing the decay of an unstable D-brane in the presence of background electric field, and explicitly evaluate the time dependence of the energy momentum tensor and the fundamental string charge density associated with this solution. The final decay product can be interpreted as a combination of stretched fundamental strings and tachyon matter.