The conformal-field-theory tag has no wiki summary.
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1answer
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+50
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
votes
3answers
87 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 ...
2
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0answers
35 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
72 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
109 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
49 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
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 ...
6
votes
1answer
75 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
64 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
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? ...
1
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0answers
57 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
votes
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
80 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
votes
1answer
84 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
vote
1answer
103 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
votes
1answer
126 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
votes
1answer
133 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
101 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 ...
8
votes
1answer
84 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 ...
1
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0answers
75 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
96 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
248 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
votes
1answer
141 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
54 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
328 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 ...
0
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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
$$S=\int d^d\! x ...
4
votes
1answer
162 views
Defining a CFT using beta-functions
Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish?
But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
4
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0answers
120 views
Trace of stress tensor vanishes ==> Weyl invariant
You often see in textbooks the statement that ${T^\mu}_\mu = 0$ implies Weyl invariance or conformal invariance. The proof goes like
$\delta S \sim \int \sqrt{g} T^{\mu\nu} \delta g_{\mu\nu} \sim ...
3
votes
1answer
74 views
How does the conformal Ward identity guarantee a vanishing 3-point function in this case?
I was looking through some conformal Ward identity related things when I noticed that this paper (arXiv:1212.3788) writes in their equation (33), a 3-point function between a conserved current and two ...
0
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0answers
52 views
A Mathematician Who Wants to Learn Particle Physics [duplicate]
Possible Duplicate:
Book recommendations
I'm a grad student in pure math, wrapping up a thesis in Lie theory. After years of talking to mathematicians and physicists, I've decided that it's ...
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2answers
233 views
Complex coordinates in CFT
The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric
$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$.
It seems to me that ...
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0answers
78 views
Massless Dirac equation is Weyl covariant
Does somebody know how to show that the following equation is Weyl invariant?
$$\gamma^ae_a^\mu D_\mu \Psi=0$$
where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
3
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1answer
94 views
Conformal Quantum Mechanics
I heard the term Conformal Quantum Mechanics used today.
What exactly does this mean?
Why would one want to study this?
3
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0answers
124 views
Inclusion of information about external particles to calculate scattering amplitudes
In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states
$$ A = \int\limits_{\rm{life time}} d\tau ...
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0answers
50 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 ...
8
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3answers
196 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
166 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
138 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 ...
8
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2answers
414 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 ...
3
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1answer
118 views
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 $U(1)$ ...
2
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1answer
110 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 ...
3
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0answers
111 views
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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0answers
63 views
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
92 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?
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1answer
116 views
Definition of CFT
A standard QFT cannot be defined as a set of Poincare-invariant correlation functions because this does not take into account the possibility of non-perturbative effects (e.g. instantons)
Can we ...
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2answers
191 views
Invariance of Maxwell's Equations under inverting variables - Reference and use
Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
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1answer
196 views
Clarification on “central charge equals number of degrees of freedom”
It's often stated that the central charge c of a CFT counts the degrees of freedom: it adds up when stacking different fields, decreases as you integrate out UV dof from one fixed point to another, ...
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105 views
Breaking of conformal symmetry
I am wondering something about the breaking of conformal symmetry: I know that it can be broken at the quantum level, anomalously, but I never encountered or heard about a model where it is broken "à ...
