Deformations of Nearly Kähler Instantons

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...

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Bibliographic Details
Published in:Communications in mathematical physics 2016-12, Vol.348 (3), p.959-990
Main Authors: Charbonneau, Benoit, Harland, Derek
Format: Article
Language:English
Subjects:
Classical and Quantum Gravitation
Complex Systems
Deformation
Instantons
Manifolds
Mathematical and Computational Physics
Mathematical Physics
Physics
Physics and Astronomy
Quantum Physics
Relativity Theory
Theoretical
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Summary: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).
ISSN:0010-3616
1432-0916
DOI:10.1007/s00220-016-2675-y