Abstract
We study the deformation theory of mathrm {G}_2-instantons on nearly mathrm {G}_2 manifolds. There is a one-to-one correspondence between nearly parallel mathrm {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 characteristic connection on the four normal homogeneous nearly mathrm {G}_2 manifolds.
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