The conformal-field-theory tag has no wiki summary.
17
votes
0answers
329 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 ...
7
votes
0answers
106 views
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 ...
6
votes
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
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 ...
4
votes
0answers
121 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 ...
4
votes
0answers
67 views
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 ...
3
votes
0answers
49 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 ...
3
votes
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 ...
3
votes
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 ...
3
votes
0answers
60 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, ...
3
votes
0answers
130 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 ...
3
votes
0answers
135 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 ...
2
votes
0answers
36 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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
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
votes
0answers
109 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 ...
2
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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
0answers
71 views
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 ...
2
votes
0answers
242 views
Trace of energy momentum tensor in $CFT_1$
There is a standard procedure to show that for CFT's in dimension $d\geq 2$, the trace of stress tensor vanishes. I think I can't apply those steps when I only have one dimension, say time, because if ...
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 ...
1
vote
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 ...
1
vote
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
...
1
vote
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 ...
1
vote
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 ...
1
vote
0answers
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 ...
1
vote
0answers
165 views
'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 ...
