In the approximation corresponding to the classical Einstein equations, which is valid at large radius, string theory compactification on a compact manifold M of G 2 or Spin(7) holonomy gives a supersymmetric vacuum in three or two dimensions. Do α ′ corrections to the Einstein equations disturb this statement? Explicitly analyzing the leading correction, we show that the metric of M can be adjusted to maintain supersymmetry. Beyond leading order, a general argument based on low energy effective field theory in spacetime implies that this is true exactly (not just to all finite orders in α ′). A more elaborate field theory argument that includes the massive Kaluza-Klein modes matches the structure found in explicit calculations. In M-theory compactification on a manifold M of G 2 or Spin(7) holonomy, similar results hold to all orders in the inverse radius of M - but not exactly. The classical moduli space of G 2 metrics on a manifold M is known to be locally a Lagrangian submanifold of H 3(M, ℝ) H 4(M, ℝ). We show that this remains valid to all orders in the α′ or inverse radius expansion.
All Science Journal Classification (ASJC) codes
- Nuclear and High Energy Physics
- Superstrings and Heterotic Strings