Kähler-Chern-Simons theory and symmetries of anti-self-dual gauge fields

V. P. Nair, Jeremy Schiff

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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 languageEnglish
Pages (from-to)329-352
Number of pages24
JournalNuclear Physics B
Issue number1-2
StatePublished - 2 Mar 1992
Externally publishedYes

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.


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