  A class of large N SU(N) gauge theories on a compact manifold S^3 X R (with
possible inclusion of adjoint matter) is known to show first order
deconfinement transition at the deconfinement temperature. This includes the
familiar example of pure YM theory and N=4 SYM theory. Here we study the effect
of introduction of N_f fundamental matter fields in the phase diagram of the
above mentioned gauge theories at small coupling and in the limit of large N
and finite N_f/N. We find some interesting features like the termination of the
line of first order deconfinement phase transition at a critical point as the
ratio N_f/N is increased and absence of deconfinement transition thereafter
(there is only a smooth crossover). This result may have some implication for
QCD, which unlike a pure gauge theory does not show a first order deconfinement
transition and only displays a smooth crossover at the transition temperature.
