The conformal-field-theory tag has no wiki summary.
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Connections and applications of SLE in physics
In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
19
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1answer
33 views
What is known about the classification of N=4 SCFTs with central charge 6?
I was talking about K3 surfaces with some physicists, and one of them told me that the N=4 superconformal field theories with central charge 6 are expected to be relatively scarce. In particular, one ...
17
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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 ...
16
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2answers
259 views
Edge theory of FQHE - Unable to produce Green's function from anticommutation relations and equation of motion?
I'm studying the edge theory of the fractional quantum Hall effect (FQHE) and I've stumbled on a peculiar contradiction concerning the bosonization procedure which I am unable to resolve. Help!
In ...
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1answer
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Miura transform for W-algebras of exceptional type
Miura transform for W-algebras of classical types can be found in e.g. Sec. 6.3.3 of Bouwknegt-Schoutens. Is there a similar explicit Miura transform for W-algebras of exceptional types, say, E6? It's ...
14
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1answer
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Do Gauge Theories (CFTs) Have Phase Transitions as the 't Hooft Coupling is Varied?
With an eye toward AdS/CFT, I'm wondering if large $N$ CFTs have a (quantum) phase transition as the 't Hooft coupling is varied. To be more specific -- if I look at correlation functions of ...
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3answers
795 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 ...
13
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2answers
128 views
Which CFTs have AdS/CFT duals?
The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any ...
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Uniqueness of supersymmetric heterotic string theory
Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about non-supersymmetric heterotic strings for now.)
The standard argument ...
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4answers
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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 ...
12
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5answers
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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 ...
12
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2answers
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How much of the Capelli-Itzykson-Zuber ADE-classification of su(2)-conformal field theories can one see perturbatively?
In their celebrated work, Capelli Itzykson and Zuber established an
ADE-classification of modular invariant CFTs with chiral algebra $\mathfrak{su}(2)_k$.
How much of that classification can one ...
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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 ...
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2answers
44 views
Examples of heterotic CFTs
I'm trying to get a global idea of the world of conformal field theories.
Many authors restrict attention to CFTs where the algebras of left and right movers agree. I'd like to increase my intuition ...
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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?
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1answer
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Conformal QFTs for D > 2
Which conformal QFTs do we know for spacetime dimension d > 2?
I know that for D = 4 we have N = 4 SYM and some N = 2 supersymmetric Yang-Mills + matter models.
What is the complete list of such ...
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4answers
570 views
Conformal transformation/ Weyl scaling are they two different things? Confused!
I see that the weyl transformation is $g_{ab} \to \Omega(x)g_{ab}$ under which Ricci scalar is not invariant. I am a bit puzzled when conformal transformation is defined as those coordinate ...
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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
258 views
AGT conjecture and WZW model
In 2009 Alday, Gaiotto and Tachikawa conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov ...
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1answer
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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 ...
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2answers
459 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 ...
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1answer
101 views
Do thermodynamic quantities in CFT correspond to something different in AdS/CFT?
From what I've (hopefully) understood from the AdS/CFT correspondence, physical quantities have a dual version. For example, the position in the bulk is the scale size (in renormalization), and waves ...
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1answer
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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 ...
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3answers
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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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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 ...
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2answers
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“tmf(n) is the space of supersymmetric conformal field theories of central charge -n”
I read this intriguing statement in John Baez' week 197 the other day, and I've been giving it some thought. The post in question is from 2003, so I was wondering if there has been any progress in ...
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1answer
748 views
What is Euler Density?
can someone please explain to me what Euler Density is? I encountered it in Weyl anomaly related issues in various articles. Most of them assumes that its familiar, but I couldn't find any accessible ...
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3answers
100 views
String-theoretic significance of extended CFT
Extended TQFT and CFT have been puzzling me for while. While I understand the mathematical motivation behind them, I don't quite understand the physical meaning. In particular, it's not clear to me to ...
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1answer
134 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 ...
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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, ...
7
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1answer
73 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 ...
7
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1answer
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Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction
I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
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Holomorphic Factorization in CFT$_2$
Is a CFT$_2$ always holomorphically factorizable? I had this idea because that's what we usually see is taken in string theory e.g (taking $z$ and $\bar{z}$ as independent variables). E.g. Ginsparg ...
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2answers
376 views
Why are conformal transformations so prevalent in physics?
What is it about conformal transformations that make them so widely applicable in physics?
These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...
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3answers
161 views
Modular invariance for higher genus
As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories:
Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
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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 ...
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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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1answer
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Poisson structure on moduli space of CFTs
The moduli space of CFTs with central charge 26 forms the classical phase space of bosonic string theory, in some sense. Similarily the moduli space of SCFTs with central charge 10 forms the classical ...
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1answer
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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 ...
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1answer
372 views
Boundary Conditions Invariant Under Conformal Transformations in Electrostatics?
in two dimensional electrostatics it is assumed that the whole physical system is translationally invariant in one direction. Here, the two-dimensional Laplace equation $$\Delta \phi(x,y) = ...
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1answer
157 views
About unitarity and R-charge in 2+1 superconformal field theory
How does unitarity require that every scalar operator in a $2+1$ SCFT will have to have a scaling dimension $\geq \frac{1}{2}$ ?
Why is an operator with scaling dimension exactly equal to ...
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0answers
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Dimensional regularization and IR divergences and scale invariance
I want to know if dimensional regularization has any issues if the theory has IR divergences or is scale invariant.
Does dimensional regularization see "all" kinds of divergences?
I mean - what ...
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3answers
62 views
which letter to use for a CFT?
In math, one says "let $G$ be a group", "let $A$ be an algebra", ...
For groups, the typical letters are $G$, $H$, $K$, ...
For algebras, the typical letters are $A$, $B$, ...
I want to say ...
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4answers
1k views
Method of Images
The method of image charges is a well-known and very useful tool for solving problems in electrostatics.
Unfortunately, when I was taught this method, it was presented simply as an algorithm. No real ...
5
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1answer
62 views
Choice and identification of vacuums in AdS/CFT
I know how we define a vacuum in flat space QFT and also in a curved space QFT. But, can somebody tell me how do the choice of vacuum state in (say) the CFT side of AdS/CFT changes the choice of ...
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2answers
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Branch-point twist fields and operator insertions on a Riemann manifold
I am having trouble understanding how Eq (2.6) in this paper (PDF)
$$Z[\mathcal{L},\mathcal{M}_{n}]\propto\langle\Phi(u,0)\tilde{\Phi}(v,0)\rangle_{\mathcal{L}^{(n)},\mathbb{R}^{2}}$$
generalizes to ...
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2answers
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Significance of massive states in string theory
A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
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1answer
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Can a $CFT_2$ which can't be factorized into chiral and antichiral parts and/or have a central charge not a multiple of 24 have AdS duals?
In the article Three dimensional gravity reconsidered by Ed Witten, he remarked that the CFT dual to three dimensional quantum gravity has to admit a holomorphic factorization and have a central ...
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1answer
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Derivation of Eq. 7.12 in the review paper of Kraus
I'm reading "Lectures on black holes and the $AdS_3/CFT_2$ correspondence" by Kraus.
http://arxiv.org/abs/hep-th/0609074
I don't know how one can obtain Eq.7.12. My stupid question is how to obtain ...
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2answers
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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 ...
