# Scalar product on the space of conformal blocks

+ 1 like - 0 dislike
139 views

Conformal blocks are extensively used as trial wave functions in the Quantum Hall Effect. The interpretation as wavefunctions implies that there is a scalar product on the space of relevant conformal blocks. Does this scalar product have any interpretation within the CFT framework, without reference to the Quantum Hall Effect?

---------------------------------------------
Addition: example for the sake of illustration and making the question more concrete. Conformal block is a function of $n$ points $B(z_1,\dots,z_n)$ which are interpreted as positions of particles in the QHE. Then for example the integral $\int d^2z_1\dots d^2z_n |B(z_1,\dots,z_n)|^2$ is a norm of the corresponding state. So, does this expression correspond to any known object in the original conformal field theory?

 Please use answers only to (at least partly) answer questions. To comment, discuss, or ask for clarification, leave a comment instead. To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL. Please consult the FAQ for as to how to format your post. This is the answer box; if you want to write a comment instead, please use the 'add comment' button. Live preview (may slow down editor)   Preview Your name to display (optional): Email me at this address if my answer is selected or commented on: Privacy: Your email address will only be used for sending these notifications. Anti-spam verification: If you are a human please identify the position of the character covered by the symbol $\varnothing$ in the following word:p$\hbar$ysi$\varnothing$sOverflowThen drag the red bullet below over the corresponding character of our banner. When you drop it there, the bullet changes to green (on slow internet connections after a few seconds). To avoid this verification in future, please log in or register.