In a general CFT, how can the identity operator be mapped into a state? Can you give examples to demonstrate the systematic way to do the mapping? Take 2D CFT (in String Theory) as examples. For X-CFT, $\hat{1}$ is mapped to the ground state $|0>_X$; for bc-CFT, $\hat{1}$ is mapped to $b_{-1}|\downarrow>_{gh}$.
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3Related : (http://physics.stackexchange.com/a/88777/6316) – Trimok Sep 30 '14 at 09:43