All Questions
Tagged with unitarityconformal-field-theory
13 questions
1vote
1answer
83views
How to prove that unit operators are the only operators with zero scaling dimension in an unitary CFT?
In David Simmons-Duffin's Phys 229 notes found on author's github here pg. 147 it is said that the free boson field $\phi$ in bosonic CFT has zero dimension but it is not the unit operator. So the ...
- 336
0votes
1answer
80views
Finiteness of the Kac table for minimal model
I am currently reading CFT from Di Francesco. I am stuck at not understanding why the kac table for minimal models $(p, q)$ where $p$ and $q$ are co-prime, only has fields with conformal dimension $h_{...
7votes
1answer
927views
What does it mean for QFT to be unitary?
I understand the statement that 'X QFT is unitary' is shorthand for saying 'the S-matrix of X QFT is unitary', cf. e.g. this Phys.SE post. Is there some definition of unitarity that is stronger than ...
- 1,062
4votes
2answers
707views
The structure of the Hilbert space of 2d CFT
In many textbooks, I found similar statements that in 2d CFT (which I hope I'm not misunderstanding), one can decompose the space of states into primaries and their Virasoro descendants, or into quas-...
- 701
0votes
1answer
793views
CFT with negative central charge
As I understand, there are CFTs with negative central charge $c<0$. It is said that such theories break unitarity. I think that the most famous theory with $c<0$ is ghost CFT with $c=-26$ (but I ...
- 5,757
3votes
0answers
129views
Why is the Weyl tensor square gravity non-unitary?
I want to understand constraints of unitarity in quantum field theory. There is quite folklore statement: gravity with a Weyl tensor square term is non-unitary How to understand this? (I think that ...
- 5,757
2votes
0answers
156views
Weyl- Squared Lagrangians
I'm studying conformal gravity theories, in particular I read that if we take $L=\sqrt{g}C_{abcd}C^{abcd}$ where $C$ is the Weyl tensor the theory we get is not unitary. What does it means unitary at ...
1vote
0answers
307views
Irrational Conformal Field Theory v.s. Non-Unitary Conformal Field Theory?
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 ...
- 4,406
2votes
1answer
522views
Unitary CFT and Kac determinant
I am currently reading the BPZ paper, and trying to understand the nature of Minimal models. We compute the Kac determinant, and it is claimed that it must be positive for the theory to be a Unitary ...
- 1,212
2votes
1answer
625views
Unitary Representations in Conformal Field Theory
So I am currently studying conformal field theory from the perspective of the representation theory of Lie algebras. I am trying to understand exactly why we care about unitarizable Verma modules. For ...
- 196
0votes
1answer
177views
If a conformal block violates unitarity, does it vanish?
When a conformal block has dimensions and spin that violate its unitarity bounds, does that make the block equal to zero? I'm asking because I'm trying to calculate 3D conformal blocks via a recursion ...
1vote
0answers
87views
Unitarity violation in 2D conformal field theory (CFT)
Why if we have a 4 point function in 2D CFT on the plane with non-OPE singularities this would be a signal of unitarity violation?
- 582
11votes
2answers
1kviews
Scale invariance plus unitarity implies conformal invariance?
What has the reaction been towards the recent paper claiming to have a proof that scale invariance plus unitarity implies conformal invariance in 4d?
- 28.8k
