Rarita-Schwinger fields on nearly parallel G2-manifolds

Abstract

We study Rarita-Schwinger fields on compact nearly parallel G2-manifolds. In order to investigate them, there is need to clarify the relationship between some differential operators for the canonical G2-connection and the Levi-Civita connection. As a result, we identify the space of Rarita-Schwinger fields with a subspace of the eigenspace of the Laplacian. Applying the same technique to the deformation theory that we use to study Rarita-Schwinger fields, we also identify the space of infinitesimal deformations of the Killing spinor. Since there is a one-to-one correspondence between nearly parallel G2-structures and Killing spinors on 7-dimensional spin manifolds, our results imply that infinitesimal deformations of nearly parallel G2-structures are examined in terms of Killing spinors.