The conformal-field-theory tag has no wiki summary.
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Conformal group in two dimensions [closed]
How can one show in a group-theoretical way that each of SO(d,2) and SO(d+1,1) is isomorphic to two-copies of Virasoro algebra for d=2?
4
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1answer
63 views
Number of Independent “Cross-ratios or Anharmonic-ratios”
The Cross-ratios or the Anharmonic-ratios are defined as,
$${r_{ij}r_{kl}}/{r_{ik}r_{jl}}, \text{ where } r_{ij}=\mod{r_i - r_j}.$$
Now the claim is: conformal symmetry implies that for computing $N$ ...
9
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1answer
123 views
When are the OPE relevant?
I've seen OPEs commonly used in 2d CFT, it's quite apparent to me that, in that case, it dresses a bridge between the algebraic and the operator formalism especially when combined with radial ordering ...
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2answers
102 views
Is there a general systematic approach how to calculate the individual terms in an operator product expansion?
Is there a general systematic procedure or approach to obtain the analytic functions $c_{ijk}$
as well as the corresponding operators $$A_i(z)$$ that appear in the operator product expansion (OPE)
$$
...
9
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1answer
215 views
Is there a “covariant derivative” for conformal transformation?
A primary field is defined by its behavior under a conformal transformation $x\rightarrow x'(x)$:
$$\phi(x)\rightarrow\phi'(x')=\left|\frac{\partial x'}{\partial x}\right|^{-h}\phi(x)$$
It's fairly ...
2
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3answers
92 views
Spherical inversion in terms of special conformal transformation
I want to consider conformal maps on suitable compactifications of $\mathbb{R}^{n}$. I know that a special conformal transformation: $$x_i\mapsto\frac{x_i-x^{2}b_i}{1-2b\cdot x+b^{2}x^{2}}$$ can be ...
3
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0answers
41 views
Identity in CFT
I heard and read couple of times reference to a certain identity in conformal field theory (maybe specific to two dimensions). The identity relates the trace of stress-energy tensor to the beta ...
7
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1answer
86 views
What exactly is meant by the conformal group of Minkowski space?
This is sort of a silly question because I'm a total beginner, and I debated whether it was better to ask here or on Math.SE. I decided on here because it's about how physicists use terminology, even ...
5
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2answers
118 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 ...
4
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0answers
62 views
How to understand Modular transformation in topological order?
Topological order in (2+1)D is described by its ground state degeneracy and the braiding statistics and topological spins of excitations. People believe that these information is all encoded in ground ...
3
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0answers
55 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 ...
6
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1answer
81 views
Motivation for the Deformed Nekrasov Partition Function
I have recently been doing research on the AGT Correspondence between the Nekrasov Instanton Partition Function and Louiville Conformal Blocks (http://arxiv.org/abs/0906.3219). When looking at the ...
3
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1answer
67 views
Spectral properties of CFT
What are the general spectral properties of CFT? I mean what is the "spectrum"/eigenvalues of CFT in 2d and d>2 spacetime dimensions? I understand the "spectrum" and "Fock space" realization of Dirac ...
4
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1answer
124 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? ...
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0answers
58 views
References for Understanding Minahan's N=4 SCFT review
This is about the same paper as this thread: Some questions about chapter I.1 (by Minahan) of the "Review of AdS/CFT Integrability" but it was never answered.
I have some different ...
2
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1answer
94 views
Symmetries in Wilsonian RG (2)
This question is related to the paper http://arxiv.org/abs/1204.5221 and is a continuation of the previous question Symmetries in Wilsonian RG
In the liked paper why do the equalities in equation ...
6
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0answers
89 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 ...
4
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1answer
87 views
Virasoro TT OPE in Polchinski's book
I'm trying to understand eq. 2.2.11 in Polchinski's first book.
He's computing
$$:\partial X^\mu(z)\partial X_\mu(z): :\partial' X^\nu(z')\partial' X_\nu(z'):$$
Now, I understand why this ...
1
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1answer
105 views
A question about defining a classical CFT
This is kind of related to this,
Defining a CFT using beta-functions
So what would be the right definition of a CFT even classically?
Is it true that classically one will call a theory scale ...
3
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1answer
133 views
What are the conserved charges related to the Virasoro generators?
I have just learned from reconsidering my demystified book, that when conformally maping the worldsheet of a closed string to the complex plain by using the transformation $z = e^{\tau + i\sigma}$ ...
7
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1answer
140 views
String theory - OPE and primary operators
First, a disclaimer: I am new to Physics SE, and I am primarily a mathematician, not a physicist. I apologise in advance for the possibly poor quality of the question, any and thank you for your ...
2
votes
1answer
105 views
Current operators for compactified CFTs
Intuitively I feel that if you compactified open bosonic strings on a product of $n$ circles such that each radius is fine-tuned to the self-dual point then the CFT of these $n$ world-sheet fields ...
4
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1answer
116 views
Name of fermionic CFT theory
I'm looking for a name or references to theories that include a stress energy tensor of the form
$$T(z)=A:\phi^\alpha\partial\phi_\alpha:(z)+B:\prod_{i=1}^{D}\phi^i:(z)$$
$\alpha=1,...,D$.
Where ...
9
votes
1answer
93 views
Radial quantization and infrared divergences
I am reading Ginspard lectures "Applied CFT" http://arxiv.org/abs/hep-th/9108028 which is not my first material on the subject. He tries to motivates radial quantization on the reason that ...
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0answers
79 views
Explicit evaluation of a radially ordered product
I am trying to understand the application of the operator product expansion to calculate the radially ordered product in the complex plain of $T_{zz}(z)\partial_w X^{\rho}(w)$ which should result in
...
2
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0answers
98 views
Conformal symmetry of Navier-Stokes?
This question is in reference to the paper arXiv:0810.1545
Can someone help understand this scaling argument and the proof(?) that there is a conformal symmetry in Navier-Stoke's equation? (..am I ...
9
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2answers
260 views
Algebraic/Axiomatic QFT vs Topological QFT
Can anybody please tell me a good source investigating the relation between Algebraic/Axiomatic Quantum Field Theory (AQFT) and Topological Quantum Field Theory (TQFT)? Or is there none?
3
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1answer
148 views
commutation of operator product expansion
In CFT, when we have an OPE:
$$O_1(z)O_2(w)=\frac{O_2(w)}{(z-w)^2}+\frac{\partial O_2(w)}{(z-w)}+...$$
this holds inside a time-ordered correlation function, so $O_1(z)O_2(w)=O_2(w)O_1(z)$. Does it ...
2
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1answer
55 views
Application of Ward identities for OPE under scaling and rotations
I think this is a very straightforward question but I don't see it right now. In Tong's notes on String theory (http://www.damtp.cam.ac.uk/user/tong/string/four.pdf) section 4.2.3 he defines the ...
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0answers
343 views
Sigma Models on Riemann Surfaces
I'm interested in knowing whether sigma models with an $n$-sheeted Riemann surface as the target space have been considered in the literature. To be explicit, these would have the action ...
1
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1answer
107 views
Interaction potential analysis from $\phi^4$ model
In this paper, the authors consider a real scalar field theory in $d$-dimensional flat Minkowski space-time, with the action given by
$$S=\int d^d\! x ...
4
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1answer
175 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 ...
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136 views
Trace of stress tensor vanishes ==> Weyl invariant
You often see in textbooks the statement that ${T^\mu}_\mu = 0$ implies Weyl invariance or conformal invariance. The proof goes like
$\delta S \sim \int \sqrt{g} T^{\mu\nu} \delta g_{\mu\nu} \sim ...
3
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1answer
75 views
How does the conformal Ward identity guarantee a vanishing 3-point function in this case?
I was looking through some conformal Ward identity related things when I noticed that this paper (arXiv:1212.3788) writes in their equation (33), a 3-point function between a conserved current and two ...
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A Mathematician Who Wants to Learn Particle Physics [duplicate]
Possible Duplicate:
Book recommendations
I'm a grad student in pure math, wrapping up a thesis in Lie theory. After years of talking to mathematicians and physicists, I've decided that it's ...
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2answers
237 views
Complex coordinates in CFT
The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric
$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$.
It seems to me that ...
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0answers
83 views
Massless Dirac equation is Weyl covariant
Does somebody know how to show that the following equation is Weyl invariant?
$$\gamma^ae_a^\mu D_\mu \Psi=0$$
where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
3
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1answer
102 views
Conformal Quantum Mechanics
I heard the term Conformal Quantum Mechanics used today.
What exactly does this mean?
Why would one want to study this?
3
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1answer
139 views
Inclusion of information about external particles to calculate scattering amplitudes
In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states
$$ A = \int\limits_{\rm{life time}} d\tau ...
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52 views
Is Wick rotation invariant under proper conformal transformations?
Is Wick rotation invariant under proper conformal transformations? Why or why not?
Does Wick rotation apply to conformal field theories? $(1-i\epsilon )T$ is not invariant under proper conformal ...
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0answers
49 views
How to express energy-momentum tensor of conformal fluid in terms of temperature?
I heard that conformal fluid has only one scaling governed by temperature, by how exactly the relation is derived between energy-momentum tensor and temperature? I will really appreciate if some ...
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3answers
201 views
Symmetries of a Free Massless Scalar in Two Dimensions
On p. 49 of Polchinski's book, he says: "Incidentally, the free massless scalar in two dimensions has a remarkably large amount of symmetry -- much more than we will have occasion to mention."
Does ...
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0answers
175 views
Definitions of the Normal Ordering Operator in CFTs and QFTs
Recall the normal ordering of bosonic operators in QFT is defined by a re-arrangement of operators to put creation operators to the left of annihilation operators in the product. This is designed to ...
2
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1answer
143 views
Tachyon vertex operator (Polchinski's book)
I would like to know how does Polchinski in his book "derive" what is the "tachyon vertex operator" (..as say stated in equation 3.6.25, 6.2.11..) I can't locate a "derivation" of the fact that ...
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455 views
What is the physical interpretation of the S-matrix in QFT?
A few closely related questions regarding the physical interpretation of the S-matrix in QFT: I am interested in both heuristic and mathematically precise answers.
Given a quantum field theory when ...
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1answer
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Question on Section 9.1.3 in “Conformal Field Theory” by Philippe Di Francesco et. al
Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al.
The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ ...
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1answer
123 views
What is the operator for the edge current of a fracional quantum Hall state?
The edge of a fractional quantum Hall state is a chiral conformal field theory. In the Laughlin case it corresponds to the chiral boson,
$$ S = \frac{1}{4\pi} \int dt dx ...
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Wilson lines, boundary conditions, surface defects of TQFTs
I asked the following question in mathematics stack exchange but I'd like to have answers from physicists too;
I have been studying (extended) topological quantum field theories (in short TQFTs) from ...
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can we cast physics as an interface to underlying structure? [closed]
I have put down a few thoughts on how we can start to see physics as an interface to underlying "structure". "Structure" is posed without its normal qualifier "Causal" and it will become more clear ...
2
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1answer
99 views
constraint on scaling dimension
How can we show that for any scalar operator $\Delta\geq1$ (where $\Delta$ is the scaling dimension)?
Where can I find a reference for reading where it comes from?
