The α′ expansion on a compact manifold of exceptional holonomy

Katrin Becker, Daniel Robbins, Edward Witten

Research output: Contribution to journalArticlepeer-review

26 Scopus citations


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.

Original languageEnglish (US)
Article number51
JournalJournal of High Energy Physics
Issue number6
StatePublished - Jun 2014
Externally publishedYes

All Science Journal Classification (ASJC) codes

  • Nuclear and High Energy Physics


  • M-Theory
  • Superstrings and Heterotic Strings


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