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) similar to T-p(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.