## Abstract

Kähler-Chern-Simons theory, which was proposed as a generalization of ordinary Chern-Simons theory, is explored in more detail. The theory describes anti-self-dual instantons on a four-dimensional Kähler manifold. The phase space is the space of gauge potentials, whose symplectic reduction by the constraints of anti-self-duality leads to the moduli space of instantons. We show that infinitesimal Bäcklund transformations, previously related to "hidden symmetries" of instantons, are canonical transformations generated by the anti-self-duality constraints. The quantum wave functions naturally lead to a generalized Wess-Zumino-Witten action, which in turn has associated chiral current algebras. The dimensional reduction of the anti-self-duality equations leading to integrable two-dimensional theories is briefly discussed in this framework.

Original language | English |
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Pages (from-to) | 329-352 |

Number of pages | 24 |

Journal | Nuclear Physics B |

Volume | 371 |

Issue number | 1-2 |

DOIs | |

State | Published - 2 Mar 1992 |

Externally published | Yes |

### Bibliographical note

Funding Information:* This research was supported in part by the US Department of Energy. * * Present address: Institute For Advanced Study, Olden Lane, Princeton, NJ 08540, USA.