Oscillating p-Branes

TL;DR

This paper constructs invariant world volume actions for p-branes using coset methods, extending Nambu-Goto actions to various symmetric spaces and supersymmetric cases, including a D=6 Minkowski space example.

Contribution

It introduces a systematic coset-based approach to derive invariant p-brane actions in different geometries and supersymmetric extensions, including new non-BPS vortex realizations.

Findings

Derived ISO(1,p+N) invariant p-brane actions in flat space.

Extended the framework to AdS spaces with SO(2,p+N) symmetry.

Presented supersymmetric p-brane actions with explicit non-BPS vortex examples.

Abstract

Coset methods are used to construct the action describing the dynamics associated with the spontaneous breaking of the Poincare symmetries of D dimensional space-time due to the embedding of a p-brane with codimension N=D-p-1. The resulting world volume action is an ISO(1,p+N) invariant generalization of the Nambu-Goto action in d=p+1 dimensional space-time. Analogous results are obtained for an AdS p-brane with codimension N embedded in D dimensional AdS space, yielding an SO(2,p+N) invariant version of the Nambu-Goto action in d=p+1 dimensional space-time. Attention is focused on a supersymmetric extension of the D=6 Minkowski space case with an embedded p=3 brane; a particular realization of which is provided by a non-BPS vortex. Here both the Nambu-Goto-Akulov-Volkov action and its dual tensor form are presented.