Supersymmetric Brane-Worlds

TL;DR

This paper constructs warped supersymmetric brane-world solutions with arbitrary cosmological constants, analyzes their properties, and proposes an effective action for brane sources that preserves supersymmetry in certain cases.

Contribution

It introduces new warped metrics solving Einstein equations with arbitrary cosmological constants and proposes an effective brane action analogous to BPS objects.

Findings

Maximally symmetric solutions with unbroken supersymmetry identified

Brane solutions generally break supersymmetry except in special cases

Proposed effective brane action resembles BPS extended objects

Abstract

We present warped metrics which solve Einstein equations with arbitrary cosmological constants in both in upper and lower dimensions. When the lower-dimensional metric is the maximally symmetric one compatible with the chosen value of the cosmological constant, the upper-dimensional metric is also the maximally symmetric one and there is maximal unbroken supersymmetry as well. We then introduce brane sources and find solutions with analogous properties, except for supersymmetry, which is generically broken in the orbifolding procedure (one half is preserved in two special cases), and analyze metric perturbations in these backgrounds In analogy with the D8-brane we propose an effective $(\hat{d}-2)$-brane action which acts as a source for the RS solution. The action consists of a Nambu-Goto piece and a Wess-Zumino term containing a $(\hat{d}-1)$-form field. It has the standard form of the action for a BPS extended object, in correspondence with the supersymmetry preserved by the solution.