# State operator correpondence and $S^1 \times S^1$ to $R^2$

+ 2 like - 0 dislike
231 views

I want to know the "state operator correspondence" in detail.

What i want to know is the correspondence of SS1 to R2 How the states and the operator match to each other?

I know that for SS1 via radial quantization one circle plays a role for time, which produce the states.

And for R2, we have operators.

But i don't know how these two (states in SS1 and operators in R2) match each other. Can you explain this in detail? (Recommendation of any references will be helpful to me!)

This post is imported from Physics StackExchange at 2016-06-02 04:57 (UTC) posted by SE User phy_math, SE users associated with first three comments below are ACuriousMind, phy_math and ACuriousMind respectively.

asked Jun 2, 2016
edited Jun 2, 2016

I'm not sure what you are asking. The state-operator correspondence of CFTs means that there is a bijection between states of the theory and operators. What do you mean with the "corresponding of SS1 to R2", and how is this supposed to relate to the state-operator correspondence?

@ACuriousMind, What i want to know how states and operator corresponds. i.e, how we know there is a bijection map between them?

The proof of the state-operator correspondence should be in every good CFT resource. Please indicate what you don't understand about it. Also, you still have not explained what role SS1 or R2 are supposed to play here.

## Your answer

 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$\hbar$y$\varnothing$icsOverflowThen 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.