The $α'$ Expansion On A Compact Manifold Of Exceptional Holonomy

Katrin Becker; Daniel Robbins; Edward Witten

doi:10.1007/JHEP06(2014)051

paper

The $α^{'}$ Expansion On A Compact Manifold Of Exceptional Holonomy

arXiv:1404.2460 · doi:10.1007/JHEP06(2014)051

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 $H^{3} (M, R) \oplus H^{4} (M, R)$ . We show that this remains valid to all orders in the $α^{'}$ or inverse radius expansion.

arXiv comment34 pp

The $α^{'}$ Expansion On A Compact Manifold Of Exceptional Holonomy

Abstract

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The $α^{'}$ Expansion On A Compact Manifold Of Exceptional Holonomy