THE CASIMIR ENERGY FOR BOSONIC P-BRANES COMPACTIFIED ON CONSTANT CURVATURE SPACE

We present the calculation of the static potential (Casimir energy) for bosonic p-branes embedded in spacetime with topology T(p) x R(d-p), T(p-q) x S2 x R(d-p) (p greater-than-or-equal-to q) or T(p-2) x (H-2/GAMMA) x R(d-p) (p greater-than-or-equal-to 2). The 1-loop and 1/d approximations are both considered. It is shown that results depend on twist. For example, for all considered cases the large d static potential becomes complex at a critical radius if all boundary conditions are twisted.