THE STATIC POTENTIAL FOR BOSONIC P-BRANES

The authors discuss recent results on the calculation of the static potential of open and toroidal p-branes with the Dirac action. The 1-loop and 1/d approximations, where d is the spacetime dimensionality, are both considered. Similar results are also presented for spherical p-branes embedded in spacetimes of topology Sp*Rd-p. For the toroidal and spherical p-branes the large d static potential becomes complex at a critical radius, which signals the breakdown of the static approximation. However, this tachyonic instability does not arise for the open p-brane, which has a pointlike ground state, just as in the classical limit. Identical results are found to hold in the cases of the Howe-Tucker and the Weyl-invariant actions.