  In this work the non-abelian gauge theory is reformulated in a local inertial
frame with the presence of a background rotation. With this new formalism the
influence of the background rotation on the color deconfinement transition for
a SU(2) pure gluon system. The KvBLL caloron, which is a color neutral and
asymptotically nontrivial solution of Yang-Mills equation at finite
temperature, is adopted to confine the color charges. With new solutions of the
caloron's constituent particles, i.e. dyons, the semi-classical potential,
which confines color charges, and the perturbative potential, induced by the
Gaussian fluctuation, have been obtained for this system under rotation. By
solving the critical temperature of confinement-deconfinement phase transition
in different computation schemes, it is found that neither the rotational
semi-classical potential nor Gaussian fluctuations can confine color charges
more tightly when the rotation becomes faster. While only a stronger coupling
constant is able to make the critical temperature increasing with angular
velocity, as that indicated in lattice simulations. And it is also found with
some particular sets of parameters, a non-monotonic dependence of the critical
temperature will be obtained in the most physically realistic case, in which
all the three factors are taken into account.
