An instanton (E, D) on a (pseudo-)hyperkähler manifold M is a vector bundle E associated with a principal G-bundle with a connection D whose curvature is pointwise invariant under the quaternionic structures of TxM,x∈M, and thus satisfies the Yang–Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on M and equivalence classes of certain holomorphic functions taking values in the Lie algebra of GC defined on an appropriate SL 2(C) -bundle over M. Our reformulation affords a streamlined proof of Uhlenbeck’s compactness theorem for instantons on (pseudo-)hyperkähler manifolds.

Devchand, C., Pontecorvo, M., Spiro, A. (2020). Instantons on hyperkähler manifolds. ANNALI DI MATEMATICA PURA ED APPLICATA, 199(2), 533-561 [10.1007/s10231-019-00890-5].

Instantons on hyperkähler manifolds

Pontecorvo M.
;
Spiro A.
2020

Abstract

An instanton (E, D) on a (pseudo-)hyperkähler manifold M is a vector bundle E associated with a principal G-bundle with a connection D whose curvature is pointwise invariant under the quaternionic structures of TxM,x∈M, and thus satisfies the Yang–Mills equations. Revisiting a construction of solutions, we prove a local bijection between gauge equivalence classes of instantons on M and equivalence classes of certain holomorphic functions taking values in the Lie algebra of GC defined on an appropriate SL 2(C) -bundle over M. Our reformulation affords a streamlined proof of Uhlenbeck’s compactness theorem for instantons on (pseudo-)hyperkähler manifolds.
Devchand, C., Pontecorvo, M., Spiro, A. (2020). Instantons on hyperkähler manifolds. ANNALI DI MATEMATICA PURA ED APPLICATA, 199(2), 533-561 [10.1007/s10231-019-00890-5].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11590/361275
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