Moduli spaces of G2 manifolds

Grigorian, Sergey

doi:10.1142/S0129055X10004132

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Moduli spaces of G2 manifolds

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Grigorian, Sergey
Quantum Gravity & Unified Theories, AEI-Golm, MPI for Gravitational Physics, Max Planck Society;

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Citation

Grigorian, S. (2010). Moduli spaces of G2 manifolds. Reviews in Mathematical Physics, 22: 1061. doi:10.1142/S0129055X10004132.

Cite as: https://hdl.handle.net/11858/00-001M-0000-0012-642D-D

Abstract

This paper is a review of current developments in the study of moduli spaces of G2 manifolds. G2 manifolds are 7-dimensional manifolds with the exceptional holonomy group G2. Although they are odd-dimensional, in many ways they can be considered as an analogue of Calabi-Yau manifolds in 7 dimensions. They play an important role in physics as natural candidates for supersymmetric vacuum solutions of M-theory compactifications. Despite the physical motivation, many of the results are of purely mathematical interest. Here we cover the basics of G2 manifolds, local deformation theory of G2 structures and the local geometry of the moduli spaces of G2 structures.