  We localize the four-dimensional N=4 super Yang-Mills theory on a four-sphere
to the two-dimensional constrained Hitchin/Higgs-Yang-Mills (cHYM) theory on a
two-sphere S^2. We show that expectation values of certain 1/8 BPS
supersymmetric Wilson loops on S^2 in the 4d N=4 SYM is captured by the 2d cHYM
theory. We further argue that expectation values of Wilson loops in the cHYM
theory agree with the prescription "two-dimensional bosonic Yang-Mills
excluding instanton contributions". Hence, we support the recent conjecture by
Drukker, Giombi, Ricci and Trancanelli on the 1/8 BPS Wilson loops on S^2 in
the 4d N=4 SYM.
