Why T_c is too high when antiferromagnetism is underestimated? --- An understanding based on the phase string effect

It is natural for a Mott antiferromagnetism in RVB description to become a superconductor in doped metallic regime. But the issue of superconducting transition temperature is highly nontrivial, as the AF fluctuations in the form of RVB pair-breaking are crucial in determining the phase coherence of the superconductivity. Underestimated AF fluctuations in a fermionic RVB state are the essential reason causing an overestimate of T_c in the same system. We point out that by starting with a {\it bosonic} RVB description where both the long-range and short-range AF correlations can be accurately described, the AF fluctuations can effectively reduce T_c to a reasonable value through the phase string effect, by controlling the phase coherence of the superconducting order parameter.