Hyperkähler cones and instantons on quaternionic Kähler manifolds

2020/02/03 by Devchand, Chandrashekar, Pontecorvo, Massimiliano, Spiro, Andrea
#14J60 #53C26 #53C28 #70S15 #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #High Energy Physics - Theory (hep-th) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2002.00933

Abstract

We present a novel approach to the study of Yang-Mills instantons on quaternionic Kähler manifolds, based on an extension of the harmonic space method of constructing instantons on hyperkähler manifolds. Our results establish a bijection between local equivalence classes of instantons on quaternionic Kähler manifolds M and equivalence classes of certain holomorphic maps on an appropriate SL₂(C)-bundle over the Swann bundle of M.

Related

• Instantons and Quaternions
• Quaternion-Kahler spaces, hyperkahler cones, and the c-map
• Yang-Mills instantons on cones and sine-cones over nearly Kähler manifolds
• Hyperkähler Nahm transform
• Hyper-Kähler instantons, symmetries, and flat spaces