The conformal-field-theory tag has no wiki summary.
12
votes
4answers
2k views
A pedestrian explanation of conformal blocks
I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
10
votes
2answers
1k views
Beginners questions concerning Conformal Field Theory
I started reading about Conformal Field Theory a few weeks ago.
I'm from a more mathematical background. I do know Quantum Mechanics/Classical Mechanics,
but I'm not really an expert when it comes ...
14
votes
3answers
794 views
Why does dilation invariance often imply proper conformal invariance?
Why does a quantum field theory invariant under dilations almost always also have to be invariant under proper conformal transformations? To show your favorite dilatation invariant theory is also ...
12
votes
5answers
1k views
What is the conserved quantity of a scale-invariant universe?
Consider that we have a system described by a wavefunction psi(x). We then make an exact copy of the system, and anything associated with it, (including the inner cogs and gears of the elementary ...
8
votes
2answers
458 views
Superconformal theories
Can anyone tell me where can I read about the notion of "short" and "long" representations? Like what they are etc.
From where can I learn the arguments which show that the bosonic subalgebra of ...
2
votes
1answer
151 views
A certain $\cal{N}=2$ superconformal theory (or is it?)
I want to look at the following theory in $1+1$ dimensions with $\Phi$ being the chiral superfield,
$L = \int d^2x d^4\theta \bar{\Phi}\Phi - \int d^2x d^2\theta \frac{\Phi^{k+2}}{k+2} - \int d^2x ...
2
votes
1answer
252 views
Generalized propagator
I don't understand how to calculate this generalized two-point function or propagator, used in some advanced topics in quantum field theory, a normal ordered product (denoted between ::) is subtracted ...
5
votes
1answer
61 views
Choice and identification of vacuums in AdS/CFT
I know how we define a vacuum in flat space QFT and also in a curved space QFT. But, can somebody tell me how do the choice of vacuum state in (say) the CFT side of AdS/CFT changes the choice of ...
3
votes
1answer
157 views
Wick Order and Radial Ordering in CFT
I am not so much familiar with the computations tools of conformal field theory, and I just run into an exercise asking to demonstrate the following formula (related to the bosonic field case):
...
6
votes
1answer
428 views
CFTs and formalizing quantum field theory
Moshe's recent questions on formalizing quantum field theory and lattices as a definition of field theory remind me of something I occasionally idly wonder about, and maybe this site can tell me the ...
6
votes
0answers
79 views
Dimensional regularization and IR divergences and scale invariance
I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.
Does dimensional regularization see "all" kinds of divergences?
I mean - what ...
5
votes
2answers
108 views
What is the exact relationship between on-shell amplitudes and off-shell correlators in AdS/CFT?
In this answer to a question, it is mentioned that in the AdS/CFT correspondence, on-shell amplitudes on the AdS side are related to off-shell correlators on the CFT side.
Can somebody explain this ...
5
votes
1answer
634 views
Some questions on Conformal Field Theory, Current algebras and the Sugawara construction
Since I don't know how to add another question to an already existing topic,
I'm opening a new thread. However I'm referring to:
Beginners questions concerning Conformal Field Theory
As noted, a ...
3
votes
1answer
286 views
A certain regularization and renormalization scheme
In a certain lecture of Witten's about some QFT in $1+1$ dimensions, I came across these two statements of regularization and renormalization, which I could not prove,
(1) $\int ^\Lambda \frac{d^2 ...
4
votes
1answer
160 views
Defining a CFT using beta-functions
Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish?
But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
4
votes
2answers
473 views
Superconformal algebra
I had earlier also asked a question about super conformal theories and I am continuing with that, now with more specific examples. I am quite puzzled with it given that I see no book explaining even ...
4
votes
2answers
244 views
Witten Index and letter partition function
I haven't seen any reference which explains these things and I am not sure of all the steps of the argument or the equations. I am trying to reproduce here a sequence of arguments that I have mostly ...
4
votes
1answer
117 views
QM with complex eigenvalues
What class of theories/physical systems own finite/infinite complex eigenvalues? I do know that e.g., quasinormal modes of BH do have complex eigenvalues, but are they finite or infinite in number? ...
4
votes
1answer
163 views
Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions
I am using the standard symbols of $V_\mu$ for the gauge field, $\lambda$ for its fermionic superpartner and $F$ and $D$ be scalar fields which make the whole thing a $\cal{N}=2$ vector/gauge ...
3
votes
0answers
48 views
Questions about classical and quantum scale invariance
This is kind of a continuation of this and this previous questions.
Say one has a free "classical" field theory which is scale invariant and one develops a perturbative classical solution for an ...
3
votes
1answer
707 views
Why/How is this Wick's theorem?
Let $\phi$ be a scalar field and then I see the following expression for the square of the normal ordered version of $\phi^2(x)$.
$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$
...
2
votes
2answers
441 views
Question on Conformal Field Theory
Since every question has to be asked in a seperate topic,
I'm asking a question refering to the following topic:
Beginners questions concerning Conformal Field Theory
In particula I'm refering to the ...
8
votes
1answer
93 views
AdS/CFT at D = 3
AdS/CFT at D = 3 (on the AdS side) seems to have some special issues which I bundled into a single question
The CFT is 2D hence it has an infinite-dimensional group of symmetries (locally). The ...
0
votes
1answer
102 views
Interaction potential analysis from $\phi^4$ model
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
0
votes
1answer
449 views
Question on dimensions of CFT operators (ref: MAGOO, hep-th/9905111)
Right now I am having this silly difficulty from the following:
BTW, Conformal dimension/scaling dimension is -ve of mass dimension ..right?
In p-63 of Magoo, after 3.15 eq, they said
a.) $\phi$ is ...
