Inflation versus collapse in brane matter

Mapping of fundamental branes to their worldsheet (ws) multiplets originating from spontaneous breaking of the Poincare symmetry is studied. The interaction Lagrangian for fields of the Nambu-Goldstone multiplet is shown to encode $R^2$ gravity on the ws. The power law $k_{p}\sim T_{p}^{\frac{3-p}{2(p+1)}}$ for the SO(D-p-1) gauge coupling $k_{p}$ as the function of the p-brane tension $T_{p}$ is assumed. It points to the presence of asymptotic freedom and confinement phases in brane matter. Their connection with collapse and inflation of the branes is discussed.