  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
Kahler 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 in [arXiv:math/0501084],
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 non-vanishing 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.
