$p$-Branes with $AdS_{p+1}$ vacuum as models of $R^2$ gravity

TL;DR

This paper explores how certain brane models with constant mean curvature can be mapped onto quadratic curvature gravity theories, revealing unstable vacuum solutions in specific membrane configurations.

Contribution

It demonstrates the mapping of brane actions to quadratic curvature gravity and analyzes the stability of their vacuum solutions.

Findings

Mapping of brane actions to quadratic gravity established

Explicit solutions for constant curvature hyper-worldsheets found

Unstable vacuum identified in membrane models in R^{1,3}

Abstract

Branes with constant mean curvature of their hyper-worldsheets of codim 1 are treated as the Nambu-Goldstone fields of the broken Poincare symmetry. Mapping of their action into quadratic curvature gravity action with spontaneously generated gravity, is shown. Equation for the brane potential extremals and its solution describing hyper-ws of constant curvature are found. For membranes in $\mathbf{R}^{1,3}$ this extremum is shown to be a saddle 3-dim. hypersurface which defines classically unstable vacuum.