The RN/CFT Correspondence Revisited

We reconsidered the quantum gravity description of the near horizon extremal Reissner-Nordstr{\o}m black hole in the viewpoint of the AdS${}_2$/CFT${}_1$ correspondence. We found that, for pure electric case, the right moving central charge of dual 1D CFT is $6Q^2$ which is different from the previous result $6 Q^3$ofleftmovingsectorobtainedbywarpedAdS$_3$\mathrm{/}CFT$_2$ description. We discussed the discrepancy in these two approaches and examined novel properties of our result.