Deformations of $\mathrm{G}_2$-instantons on nearly $\mathrm{G}_2$ manifolds

Ragini Singhal

doi:10.1007/s10455-022-09853-1

paper

Deformations of $G_{2}$ -instantons on nearly $G_{2}$ manifolds

arXiv:2101.02151 · doi:10.1007/s10455-022-09853-1

Abstract

We study the deformation theory of $G_{2}$ -instantons on nearly $G_{2}$ manifolds. There is a one-to-one correspondence between nearly parallel $G_{2}$ structures and real Killing spinors, thus the deformation theory can be formulated in terms of spinors and Dirac operators. We prove that the space of infinitesimal deformations of an instanton is isomorphic to the kernel of an elliptic operator. Using this formulation we prove that abelian instantons are rigid. Then we apply our results to describe the deformation space of the canonical connection on the four normal homogeneous nearly $G_{2}$ manifolds.

Updated some integrability results for the infinitesimal deformations found. All comments are welcome

Deformations of G2​-instantons on nearly G2​ manifolds

Abstract

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Deformations of $G_{2}$ -instantons on nearly $G_{2}$ manifolds