I have been reading https://arxiv.org/abs/hep-th/9702015 by Maldacena and Strominger. Authors derive emission rate of Kerr-Newmann black hole via standard asymptotic matching first. Then rederive it (sort of) from effective string picture in section 2.12. In doing so they use:

$$ \langle \mathcal{O}^{\dagger}(0)\mathcal{O}(\sigma^+)\rangle_{T_H}\sim \left[\frac{\pi T_{H}}{\sinh{(\pi T_{H}\sigma^+)}}\right]^{2\Delta} $$ given by equation 2.56 in the manuscript. Where does the above relation come from ?

Also, I am a stranger to CFT. I would appreciate if you could point me to some references on so called Effective string picture which is the theme of the section 2.12


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