On the effective action of a space-like brane

TL;DR

This paper derives an effective action for space-like branes from non-BPS D-branes, revealing differences in the action's reality depending on whether it describes an S-brane or E-brane in string theory.

Contribution

It introduces a new derivation of the effective action for space-like branes using fluctuations around tachyonic kink solutions, clarifying the role of the Wess-Zumino term in different string theories.

Findings

The WZ term is purely imaginary for S-branes and real for E-branes.

The DBI part of the action matches previous results obtained by different methods.

The effective action describes the dynamics of space-like branes in various string theory backgrounds.

Abstract

Starting from the non-BPS D$(p+1)$-brane action we derive an effective action in $(p+1)$ space dimensions by studying the fluctuations of various bosonic fields around the time-like tachyonic kink solution (obtained by Wick rotation of the space-like tachyonic kink solution) of the non-BPS brane. In real time this describes the dynamics of a space-like or Euclidean brane in $(p+1)$-dimensions containing a Dirac-Born-Infeld part and a Wess-Zumino part. The WZ part is purely imaginary and so the action is complex if it represents the source of the time-dependent background of type II string theory i.e. the S-brane. On the other hand, the WZ part as well as the action is real if it represents the source in type II$^\ast$ string theory i.e. the E-brane. The DBI part is the same as obtained before using different method. This is then further illustrated by considering brane probe in space-like brane background.