Deformations of nearly Kähler instantons

Abstract

We formulate the deformation theory for instantons on nearly Kähler six-manifolds using spinors and Dirac operators. Using this framework we identify the space of deformations of an irreducible instanton with semisimple structure group with the kernel of an elliptic operator, and prove that abelian instantons are rigid. As an application, we show that the canonical connection on three of the four homogeneous nearly Kähler six-manifolds G/H is a rigid instanton with structure group H. In contrast, these connections admit large spaces of deformations when regarded as instantons on the tangent bundle with structure group SU(3).

Communications in Mathematical Physics 2016

References in corpus (2)

• Chern-Simons flows on Aloff-Wallach spaces and Spin(7)-instantons
• Octonions, Monopoles, and Knots

Cited by in corpus (8)

• The infinitesimal moduli space of heterotic $G_2$ systems
• Deformation theory of nearly Kähler manifolds
• Gauge theory on Aloff-Wallach spaces
• Left-invariant Einstein metrics on $S^3\times S^3$
• Deformations of ${\mathrm{G}}_2$-instantons on nearly ${\mathrm{G}}_2$ manifolds
• $G_2$-instantons on the spinor bundle of the 3-sphere
• Deformation Theory of Asymptotically Conical Spin(7)-Instantons
• The DT-instanton equation on almost Hermitian 6-manifolds