Register

Adv. Query

Q&A (4871)

Reviews (203)

Open problems (47)
Meta (439)

Site Statistics

206 submissions , 164 unreviewed
5,103 questions , 2,249 unanswered
5,355 answers , 22,797 comments
1,470 users with positive rep
820 active unimported users
More ...

Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?

1121 views

Unitary conformal field theories (CFTs) with irrational (or including the special case of rational) central charge is called irrational conformal field theory (ICFT).

Irrational conformal field theory (ICFT) is said to include all conformal field theories, and, in particular, ICFT includes rational conformal field theory (RCFT).

ICFT $\supset$ RCFT.

RCFT is only a tiny subset inside ICFT.

However, do we have examples of non-unitary Conformal Field Theory (NUCFT)? If so, what are the relations between:

unitary RCFT
unitary ICFT
non-unitary RCFT
non-unitary ICFT

Are there good quantum mechanical lattice realizations of these CFTs?

What are the relations of their sets?

This post imported from StackExchange Physics at 2020-11-26 15:39 (UTC), posted by SE-user annie marie heart

asked Sep 5, 2019 in Theoretical Physics by annie marie heart (1,205 points) [ no revision ]

unitarity at $c<1$ implies rationality, no?

This post imported from StackExchange Physics at 2020-11-26 15:39 (UTC), posted by SE-user AccidentalFourierTransform

commented Sep 5, 2019 by AccidentalFourierTransform (480 points) [ no revision ]

Rational theories are, generally speaking, theories which have finite number of primaries of their respective chiral algebras (in the simplest case of Virasoro algebra, but one can have Kac-Moody algebras, etc.), although there may be people with stronger and/or more abstract opinions on this term. Also, there exist non-unitary theories, which can be rational or non-rational. I don't know whether anything useful can be said beyond these two facts.

This post imported from StackExchange Physics at 2020-11-26 15:39 (UTC), posted by SE-user Peter Kravchuk

commented Sep 5, 2019 by Peter Kravchuk (40 points) [ no revision ]

Also, your definitions are not consistent. You define ICFT to have irrational central charge, and then you say that RCFT is a special case of ICFT. It can't be since RCFT's have rational central charges.

This post imported from StackExchange Physics at 2020-11-26 15:39 (UTC), posted by SE-user Peter Kravchuk

commented Sep 5, 2019 by Peter Kravchuk (40 points) [ no revision ]

Minimal models and Liouville theory provide examples of rational and non-rational CFTs, which can be unitary or not depending on the central charge. See Wikipedia.

This post imported from StackExchange Physics at 2020-11-26 15:39 (UTC), posted by SE-user Sylvain Ribault

commented Sep 5, 2019 by Sylvain Ribault (0 points) [ no revision ]

Your comment on this question:

To answer, leave an answer instead. Comments are usually for non-answers.
To mask links under text, please type your text, highlight it, and click the "link" button. You can then enter your link URL.
To alert a user, please use the "@" command and remove spaces from the username, example, the user "John Doe" should be pinged as "@JohnDoe", while the user "Johndoe" should be pinged as "@Johndoe". The post author is always automatically pinged (unless you are the post author).
Please consult the FAQ for as to how to format your post.

Live preview (may slow down editor) Preview

Your name to display (optional):

Email me at this address if a comment is added after mine:

Privacy: Your email address will only be used for sending these notifications.

Anti-spam verification:

[captcha placeholder]

Please complete the anti-spam verification

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$\hbar\varnothing$sicsOverflow
Then 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).

Please complete the anti-spam verification

user contributions licensed under cc by-sa 3.0 with attribution required

Your rights

...