The conformal-field-theory tag has no wiki summary.
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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
206 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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208 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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111 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 ...
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1answer
144 views
2D Ghost CFT and two-point functions
For some reason I am suddenly confused over something which should be quit elementary.
In two-dimensional CFT's the two-point functions of quasi-primary fields are fixed by global $SL(2,\mathbb ...
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4answers
628 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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70 views
How can we have massive states of strings and CFT on the string worldsheet at the same time?
Ok, so we can have conformal invariance on a string world sheet. However, it is well known that to preserve conformal symmetry we require states to be massless. So how is it that string theories ...
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1answer
127 views
Conformal Invariance and the OPE
I am reading Polchinski's String Theory now and am having trouble with a couple of things mentioned on Page 45 under "Conformal Invariance and the OPE". Here is the paragraph I am reading. The ...
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1answer
196 views
Equivalent definitions of primary fields in CFT
I have come across two similar definitions of primary fields in conformal field theory. Depending on what I am doing each definition has its own usefulness. I expect both definitions to be compatible ...
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't Hooft's landscape of conformally constrained QFTs
As described in "A class of elementary particle models without any adjustable real parameters", "The Conformal Constraint in Canonical Quantum Gravity", and "Probing the small distance structure of ...
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1answer
121 views
Constraining two-point functions of boundary operators on the disk
I'm trying to understand the constraints on the disk CFT correlation function $\langle O_1(y_1)O_2(y_2)\rangle$, where the $O_i$'s are boundary operators that are not necessarily primary. It's a ...
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Derivation of the enhancement of U(1)$_L$ x U(1)$_R$ to SU(2)$_L$ x SU(2)$_R$ at the self-dual radius
Towards the end of the paragraph with the title String theory's added value 2: enhanced non-Abelian symmetries at self-dual radii and abstract C with current algebras of this article, it is explained ...
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Exercise QFT and CFT
Consider the action functional
$S[z;t_1,t_2]=\int_{t_1}^{t^2}[g(z,\bar{z})\dot{z}\dot{\bar{z}}]^{\frac{1}{2}}dt$
with $z(t)$ a complex path with end points $z_i=z(t_i),\; i=1,2$. $g(z,\bar{z})$ is a ...
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1answer
113 views
1-Dimensional Sigma Models
I'm currently interested in 1-dimensional (linear) Sigma Models.
In the theory of 2-Dimensional GLSM, the fields can be viewed as an embedding of the worldsheet in some target Manifold of higher ...
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61 views
Relating the deformation of Calabi-Yau metrics and the conformal quantum field theories
(v2)
As I read e.g. in this question, the nice holonomy group features of Calabi-Yau manifolds are valuable regarding supersymmetry (I suspect because it's a symmetry involving the target manifold, ...
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80 views
The neutrality condition and the (non)-vanishing of the one-point correlator for the bosonic vertex operator
Consider the massless scalar field Hamiltonian,
\begin{align}
H = \frac{1}{2}\int \Pi^2- (\partial_x\phi)^2 dx
\end{align}
with $\Pi \sim \partial_t\phi$ the conjugate field of $\phi$. This ...
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1answer
146 views
Conformal fields on compactified manifolds? An apparent paradox!
I would appreciate it if someone tells me how a cft on a compactified manifold (e.g. by means of periodic boundary conditions) can be meaningful? The global conformal invariance is broken due to the ...
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Defects in 3+1 TFTs/2+1 CFTs
I would like to know of good pedagogic references to learn about the notion of "defects" in TFTs and CFTs. I am specially interested in 3+1 TFTs (.and probably about their relation to 2+1 CFTs..)
In ...
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132 views
Central charge at the fixed point of the ${\cal N}=2$ Landau-Ginzburg theory in $1+1$ dimensions
Let me first believe that the ${\cal N}=2$ Landau-Ginzburg theory does in the IR flow to a non-trivial fixed point and that if the potential is of the form $\Phi ^k$ then the central charge of the CFT ...
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1answer
295 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 ...
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137 views
Toda equations and surface operator
I would like to know the reason why the equation (14) in the paper by Yamada is called the Toda equation.
\begin{equation}
\left[\frac12\sum_{i=1}^N\left(y_i\frac{\partial}{\partial ...
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1answer
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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 ...
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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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52 views
Scale invariance Vs Conformal invariance [duplicate]
Possible Duplicate:
Why does dilation invariance often imply proper conformal invariance?
What exactly is the difference between the two. Can someone give an example of a theory which is ...
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1answer
131 views
Electromagnetic current-current correlators
Let the free electromagnetic current $J_\mu(x)$ be = $:\bar{\psi}(x)\gamma_\mu Q \psi(x):$ where $::$ is the normal ordering.
In this expression why is $Q$ thought of as a "charge operator" instead ...
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1answer
320 views
What is the meaning of the concepts of “operator mixing” (and anomalous dimensions) [closed]
I am looking for an explanation about the idea of "operator mixing" and its associated concept about when anomalous dimension has to be thought of as a matrix.
For example this idea is slightly ...
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1answer
741 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 $\phi^2(x)$.
$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$
...
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1answer
162 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):
...
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2answers
219 views
How are functional determinants of Laplace-type operators used in physics?
Many mathematical papers concerning the $\zeta$-regularized Determinant of Laplace-type operators refer for motivation to the broad use of such determinants in mathematical physics, especially in ...
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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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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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57 views
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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3answers
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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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190 views
Conformal transformation equation
I am currently reading Kiritsis's string theory book, and something bugs in the CFT (fourth) chapter. He derives the equation that should satisfy an infinitesimal conformal transformation $x^{\mu} ...
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Significance of massive states in string theory
A free superstring has an infinite tower of states with increasing mass. The massless states correspond to the fields of the corresponding SUGRA. In "Quantum Fields and Strings: A Course for ...
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Modular invariance for higher genus
As far as I understand, there are roughly 2 "common" kinds of 2D conformal field theories:
Theories that are defined only on the plane, more precisely, on any surface of vanishing genus. Such a ...
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Holomorphic Factorization in CFT$_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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How to construct a 2D conformal field on a mirrored annulus with a looping pattern?
I would like to construct a 2D conformal field on an annulus in which the inner and outer boundaries are like mirrors, and can be approximated by regular polygons (with the same number n of mirror ...
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1answer
118 views
Do a 1-dimensional conformal theory exist?
can we have in physic or can we speak about 1-d conformal theory in physics ??
for example in this one dimensional theory what would be the generators $ x \partial _{x} $ or $ \partial _{x} $ ??
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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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“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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324 views
Why is a critical quantum system described by a conformal theory in one higher dimension of space?
These questions are linked, so I've asked them in a single post:
Why is a critical one-dimensional many-body system a two-dimensional conformal field theory?- Why the switch from 1D to 2D?
What does ...
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1answer
257 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 ...
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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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Massive excitations in Conformal Quantum Field Theory
Single particle states in quantum field theory appear as discrete components in the spectrum of the Poincare group's action on the state space (i.e. in the decomposition of the Hilbert space of ...
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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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360 views
Special conformal transformations and locality
In the conformal symmetry, used in some QFT theories, the infinitesimal generators, applying to space-time, are all linear (translations, rotations, boosts, dilatation), except the special conformal ...
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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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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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412 views
Explanation of Cardy's “a theorem”
There seems to have been some discussion of Cardy's "a-theorem" recently:
“It is shown that, for d even, the one-point function of the trace of the stress tensor on the sphere, Sd, when suitably ...
