Dynamical Compactification of D-Dimensional Gravity Coupled to Antisymmetric Tensors in a 1/D Expansion

摘要

The effective potential of components of the curl of an antisymmetric tensor coupled to gravity in D dimensions is evaluated in a 1/D expansion. For large D, only highest-rank propagators contribute to leading order, while multiloop diagrams are suppressed by phase-space factors. Divergences are regulated by a cut-off lambda, that we interpret as the mass-breaking scale of a larger theory that is finite. As an application we consider the bosonic sector of D=11, N=1 supergravity. If the full theory is finite, then lambda is msub(SUSY): the scale below which the fermion sector decouples. For m exp 9 sub(SUSY) > 1/akappa exp 2 , (kappa exp 2 : the D=11 Newton's coupling, a approx.= O(1)) the 11-dimensional symmetric vacuum is unstable under compactification. For m exp 9 sub(SUSY) <= 1/akappa exp 2 , it is metastable. To leading order in 1/D, all gauge dependence cancels identically, while ghosts as well as the graviton decouple. (Atomindex citation 16:078645)