Static, non-SUSY $p$-branes in diverse dimensions

TL;DR

This paper constructs explicit static, non-supersymmetric p-brane solutions in various dimensions, exploring their properties, interpolations between different solution types, and connections to known BPS solutions and time-dependent cases.

Contribution

It provides new explicit static non-SUSY p-brane solutions in diverse dimensions, including interpolations and relations to BPS and time-dependent solutions.

Findings

Solutions interpolate between p-brane--anti p-brane and BPS p-branes.

Some solutions are near horizon limits of known BPS p-branes.

Time-dependent solutions relate via Wick rotation to static solutions.

Abstract

We give explicit constructions of static, non-supersymmetric $p$-brane (for $p \leq d-4$, where $d$ is the space-time dimensionality and including $p=-1$ or D-instanton) solutions of type II supergravities in diverse dimensions. A subclass of these are the static counterpart of the time dependent solutions obtained in [hep-th/0309202]. Depending on the forms of the non-extremality function $G(r)$ defined in the text, we discuss various possible solutions and their region of validity. We show how one class of these solutions interpolate between the $p$-brane--anti $p$-brane solutions and the usual BPS $p$-brane solutions in $d=10$, while the other class, although have BPS limits, do not have such an interpretation. We point out how the time dependent solutions mentioned above can be obtained by a Wick rotation of one class of these static solutions. We also discuss another type of solutions which might seem non-supersymmetric, but we show by a coordinate transformation that they are nothing but the near horizon limits of the various BPS $p$-branes already known.