In this paper, we study the perturbative aspects of the half-twisted
variant of Witten’s topological A-model coupled to a non-dynamical
gauge field with Kähler target space X being a G-manifold. Our main
objective is to furnish a purely physical interpretation of the equivariant
cohomology of the chiral de Rham complex, recently constructed
by Lian and Linshaw, called the “chiral equivariant cohomology.”
In doing so, one finds that key mathematical results such as the vanishing
in the chiral equivariant cohomology of positive weight classes,
lend themselves to straightforward physical explanations. In addition,
one can also construct topological invariants of X from the correlation
functions of the relevant physical operators corresponding to the nonvanishing
weight-zero classes. Via the topological invariance of these
correlation functions, one can verify, from a purely physical perspective,
the mathematical isomorphism between the weight-zero subspace of the
chiral equivariant cohomology and the classical equivariant cohomology
of X. Last but not least, one can also determine fully, the de Rham
cohomology ring of X/G, from the topological chiral ring generated by
the local ground operators of the physical model under study.