Abstract
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,\( \mathbb{R} \)) ⊕ H 4(M,\( \mathbb{R} \)). We show that this remains valid to all orders in the α ′ or inverse radius expansion.
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ArXiv ePrint: 1404.2460
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Becker, K., Robbins, D. & Witten, E. The α ′ expansion on a compact manifold of exceptional holonomy. J. High Energ. Phys. 2014, 51 (2014). https://doi.org/10.1007/JHEP06(2014)051
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DOI: https://doi.org/10.1007/JHEP06(2014)051