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We correlate the weak gravity conjecture (WGC), the KSS conjecture withchemical potential at extremality and the central charges by going through aparticular example in five dimensional AdS spacetime with two unknowncoefficients $c_1, c_2$, assuming WGC exists in AdS spacetime. The result thatfollows from this example suggests that WGC makes the KSS conjecture to hold inthe extremal limit but only when one of the coefficient vanishes ($c_1=0,c_2\neq 0$ or $c_2=0, c_1\neq 0$) and when both the coefficients are non zeroit can respect and/or violate the KSS conjecture depending on the choice to$c_1$ at extremality, even though $\eta/s$ do not depend on $c_1$ atextremality. Moreover, WGC is not fully compatible with the calculation ofcentral charges even though the bounds on coefficient $c_1$ that follows fromdemanding WGC stays within the bounds that central charges predict. As usual,the KSS conjecture is violated, of course, in the non-extremal limit.

Weak Gravity Conjecture, Central Charges and $\eta/s$