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Typographical correction: In the character of the Ishibashi state that gives the matter partition function, the denominator is $\eta$, not $\eta^c$; i.e., the matter partition function is $\chi_{matter} = {q^{E_m} \over \eta}$. The eta function comes from the tower of Virasoro descendants. Note that the eta functions then cancel between Liouville, ghosts, and matter.

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