The SL(2,C) Yang–Mills instanton solutions constructed recently by the biquaternion method were shown to satisfy the complex version of the ADHM equations and the monad construction. Moreover, we discover that, in addition to the holomorphic vector bundles on CP3 similar to the case of SU(2) ADHM construction, the SL(2,C) instanton solutions can be used to explicitly construct instanton sheaves on CP3. Presumably, the existence of these instanton sheaves is related to the singularities of the SL(2,C) instantons on S4 which do not exist for SU(2) instantons.
- Biquaternion ADHM construction
- Instanton sheaves
- Monad construction
- SL(2,C) Yang–Mills instanton
- Singularities of gauge fields