String and M-theory Deformations of Manifolds with Special Holonomy

TL;DR

The work shows that string/M-theory ${\alpha'}^3$ $R^4$ corrections deform internal manifolds with Spin(7) and SU(5) holonomy but can preserve supersymmetry through a corrected gravitino transformation. It derives a universal, purely Riemannian form for the supersymmetry-violating terms and provides explicit first-order deformations for Spin(7) and non-compact SU(5) backgrounds, including Minkowski3×K8 and Minkowski1×K10 cases, with warp factors and nonzero F4s. The results extend prior G2 analyses, confirm SUSY via a modified covariant derivative $D_i=\nabla_i+Q_i$, and illustrate SUSY preservation in explicit examples like S^7 and Aloff–Wallach spaces, while addressing topological constraints in compact settings. Overall, the paper reinforces the resilience of supersymmetric compactifications under higher-derivative corrections and offers a coherent framework for their Riemannian corrections.

Abstract

The R^4-type corrections to ten and eleven dimensional supergravity required by string and M-theory imply corrections to supersymmetric supergravity compactifications on manifolds of special holonomy, which deform the metric away from the original holonomy. Nevertheless, in many such cases, including Calabi-Yau compactifications of string theory and G_2-compactifications of M-theory, it has been shown that the deformation preserves supersymmetry because of associated corrections to the supersymmetry transformation rules, Here, we consider Spin(7) compactifications in string theory and M-theory, and a class of non-compact SU(5) backgrounds in M-theory. Supersymmetry survives in all these cases too, despite the fact that the original special holonomy is perturbed into general holonomy in each case.