Tagged Questions
9
votes
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 ...
5
votes
2answers
117 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 ...
3
votes
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
votes
1answer
80 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 ...
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
votes
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 ...
1
vote
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 ...
9
votes
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?
18
votes
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
vote
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
$$S=\int d^d\! x ...
4
votes
1answer
175 views
Defining a CFT using beta-functions
Won't it be correct to define a CFT as a QFT such that the beta-function of all the couplings vanish?
But couldn't it be possible that the beta-function of a dimensionful coupling vanishes but it ...
4
votes
0answers
136 views
Trace of stress tensor vanishes ==> Weyl invariant
You often see in textbooks the statement that ${T^\mu}_\mu = 0$ implies Weyl invariance or conformal invariance. The proof goes like
$\delta S \sim \int \sqrt{g} T^{\mu\nu} \delta g_{\mu\nu} \sim ...
6
votes
2answers
237 views
Complex coordinates in CFT
The Setup: Let's say we want to study a Euclidean $\mathrm{CFT}_2$ on $\mathbb R^2$ with coordinates $\sigma^1$ and $\sigma^2$ and metric
$ds^2 = (d\sigma^1)^2+(d\sigma^2)^2$.
It seems to me that ...
1
vote
0answers
83 views
Massless Dirac equation is Weyl covariant
Does somebody know how to show that the following equation is Weyl invariant?
$$\gamma^ae_a^\mu D_\mu \Psi=0$$
where: $D_\mu \Psi=\partial_\mu\Psi+A_\mu^{ab}\Sigma_{ab}\Psi$ is the spin-covariant ...
3
votes
1answer
139 views
Inclusion of information about external particles to calculate scattering amplitudes
In this (schematic) equation to calculate the scattering amplitude A by integrating over all possible world sheets and lifetimes of the bound states
$$ A = \int\limits_{\rm{life time}} d\tau ...
2
votes
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
votes
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 ...
8
votes
2answers
453 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
votes
0answers
112 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 ...
2
votes
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?
1
vote
1answer
117 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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
0answers
112 views
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 ...
1
vote
1answer
151 views
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 ...
2
votes
0answers
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 ...
2
votes
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 ...
3
votes
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 ...
5
votes
2answers
200 views
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 ...
2
votes
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 ...
1
vote
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 ...
3
votes
1answer
739 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 $\phi^2(x)$.
$$T(:\phi^2(x)::\phi^2(0):) ~=~ 2<0|T(\phi(x)\phi(0))|0>^2 $$
...
6
votes
3answers
168 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 ...
2
votes
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 ...
9
votes
1answer
73 views
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 ...
4
votes
1answer
91 views
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 ...
4
votes
3answers
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 ...
10
votes
2answers
46 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 ...
5
votes
1answer
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 ...
16
votes
2answers
263 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 ...
3
votes
1answer
229 views
String matrix models with c>1
Question 1: What is the status of string random matrix models (~ triangulated random surfaces) with c>1?
In my limited search, I have just come across a few papers by Frank Ferrari (in 2000-2002) on ...
2
votes
1answer
392 views
How do you obtain the commutation relations at non-equal times (for the edge of a fractional quantum Hall state)?
The edge of a fractional quantum Hall state is an example of a chiral Luttinger liquid. Take, for the sake of simplicity, the edge of the Laughlin state. The Hamiltonian is:
$$H = ...
6
votes
1answer
158 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 ...
2
votes
0answers
122 views
Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions -Part 2
This is in continuation to what I was asking here earlier -
Argument for quantum theoretic conformality of $\cal{N}=2$ super-Chern-Simon's theory in $2+1$ dimensions
Or one can look at this ...
4
votes
1answer
165 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
1answer
200 views
Superpartner for the stress-energy tensor
I would like to understand what is meant when one introduces a generator $G(z)$ as the superpartner of the energy-momentum tensor $T(z)$.
How does one decide that this $G(z)$ should have a ...
5
votes
1answer
642 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 ...
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 ...
7
votes
1answer
768 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 ...
