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Kähler-Chern-Simons Theory And Symmetries Of Anti-Self-Dual Gauge Fields

By V. Parameswaran Nair and Jeremy Schiff


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 in-stantons 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 framewor

Topics: Physical Sciences and Mathematics, Physics
Publisher: CUNY Academic Works
Year: 1991
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