Instantons in six dimensions and twistors

authored by

Tatiana A. Ivanova, Olaf Lechtenfeld, Alexander D. Popov, Maike Tormählen

Abstract

Recently, conformal field theories in six dimensions were discussed from the twistorial point of view. In particular, it was demonstrated that the twistor transform between chiral zero-rest-mass fields and cohomology classes on twistor space can be generalized from four to six dimensions. On the other hand, the possibility of generalizing the correspondence between instanton gauge fields and holomorphic bundles over twistor space is questionable. It was shown by Sämann and Wolf that holomorphic line bundles over the canonical twistor space Tw(X) (defined as a bundle of almost complex structures over the six-dimensional manifold X) correspond to pure-gauge Maxwell potentials, i.e. the twistor transform fails. On the example of X=CP3 we show that there exists a twistor correspondence between Abelian or non-Abelian Yang-Mills instantons on CP3 and holomorphic bundles over complex submanifolds of Tw(CP3), but it is not so efficient as in the four-dimensional case because the twistor transform does not parametrize instantons by unconstrained holomorphic data as it does in four dimensions.

Organisation(s)

Institut für Theoretische Physik
Riemann Center for Geometry and Physics
Quest: Centre for Quantum Engineering and Space-Time Research

External Organisation(s)

Joint Institute for Nuclear Research (JINR)

Type

Artikel

Journal

Nuclear Physics B

Volume

882

Pages

205-218

No. of pages

14

ISSN

0550-3213

Publication date

05.2014

Publication status

Veröffentlicht

Peer reviewed

Yes

ASJC Scopus Sachgebiete

Kern- und Hochenergiephysik

Electronic version(s)

https://doi.org/10.1016/j.nuclphysb.2014.02.023 (Access: Offen)