Supersymmetric Deformations of G2 Manifolds from Higher-Order Corrections to String and M-Theory

The equations of 10 or 11 dimensional supergravity admit supersymmetric compactifications on 7-manifolds of G2 holonomy, but these supergravity vacua are deformed away from special holonomy by the higher-order corrections of string or M-theory. We find simple expressions for the first-order corrections to the Einstein and Killing spinor equations in terms of the calibrating 3-form of the leading-order G2-holonomy background. We thus obtain, and solve explicitly, systems of first-order equations describing the corrected metrics for most of the known classes of cohomogeneity one 7-metrics with G2 structures. 1 Research supported in part by DOE grant DE-FG03-95ER40917 2 Research supported in part by the EC under TMR contract HPRN-CT-2000-00131 and by PPARC under SPG grant PPA/G/S/1998/00613. 3 On leave from DAMTP, University of Cambridge, UK.