Vacuum energy in the presence of dielectric and conducting surfaces: P. Candelas. Center for Theoretical Physics, The University of Texas at Austin, Austin, Texas 78712

Abstract

We study (4 + d)-dimensional Einstein-Yang-Mills theories with arbitrary gauge groups, GYM. The theory is compactified on a d-dimensional symmetric coset space GH with a symmetric, topologically non-trivial classical gauge field, embedded in an H-subgroup of the Yang-Mills group. These theories are known to be classically stabilized by gravity if GYM = H, GH is a sphere and d ≠ 3. We study classical instabilities caused by embedding H in a larger gauge group. The small fluctuation spectrum is completely calculable, and leads to a stability condition. For two-dimensional spheres this condition is precisely the Brandt-Neri stability condition for non-abelian monopole fields. For four-spheres we find stability for SU(2) instantons embedded in arbitrary gauge groups and we reproduce the fluctuation spectrum around instantons. For higher-dimensional spheres the stable solutions of this type are completely classified, and occur only for d = 5, 6, 8, 9, 10, 12 and 16. The results show a remarkable agreement with expected topological stability. We also give a few examples with other symmetric spaces, such as CPn, where the stability criterion appears less restrictive.