K\"ahler-Chern-Simons Theory

TL;DR

This paper explores Kähler-Chern-Simons theory, focusing on its geometric structure, symmetries, and quantum properties, and discusses its connection to integrable systems through dimensional reduction.

Contribution

It provides a detailed analysis of the symmetries, phase space, and quantum aspects of Kähler-Chern-Simons theory, linking it to integrable systems.

Findings

Characterization of the phase space as gauge potentials

Identification of symmetries and their canonical realization

Discussion of quantum wave functions and integrable systems connection

Abstract

K\"ahler-Chern-Simons theory describes antiself-dual gauge fields on a four- dimensional K\"ahler manifold. The phase space is the space of gauge potentials, the symplectic reduction of which by the constraints of antiself-duality leads to the moduli space of antiself-dula instantons. We outline the theory highlighting the symmetries, their canonical realization and some properties of the quantum wave functions. The relationship to integrable systems via dimensional reduction is briefly discussed.