A conformal field theory (CFT) is a quantum field theory that is invariant under conformal transformations. In 2D, the infinite-dimensional algebra of local conformal transformations normally permits exact solution or classification of such theories. Further use for CFT applications to string ...

learn more… | top users | synonyms (2)

0
votes
0answers
9 views

AdS3/CFT2 duality for free bulk scalar

I am looking at lecture notes by Kaplan. http://www.pha.jhu.edu/~jaredk/AdSCFTCourseNotesPublic.pdf Through chapters 4, 5, and 6 he takes the free field in AdS3 to the boundary to create a CFT2 ...
1
vote
0answers
19 views

Special conformal transformation of stress-energy

Consider a 2d CFT, e.g. a single bosonic degree of freedom. The $TT$ OPE is $$ T(w) T(z) = \frac{c/2}{(z-w)^4} + \frac{2 T(w)}{(z-w)^2} + \frac{\partial T(w)}{z-w} + \text{regular terms}. $$ Does ...
0
votes
1answer
28 views

Relation of conformal symmetry and traceless energy momentum tensor

In usual string theory, or conformal field theory textbook, they states traceless energy momentum tensor $T_{a}^{\phantom{a}a}=0$ implies (Here energy momentum tensor is usual one which is symmetric ...
2
votes
0answers
46 views

Correlation function for ghosts in 2D CFT

In Di Fracenso, page 117, it is explained that the correlation function for two primary fields $\phi_1,\phi_2$ of weights $h_1,h_2$ is constrained to be of the form ...
1
vote
2answers
47 views

In a 2D CFT of a free boson $X$, is $X$ a primary field?

A primary field $\mathcal{O}(w,\bar{w})$ with weight $(h,\bar{h})$ is defined by having the following OPEs with the stress tensor: ...
0
votes
0answers
29 views

What is known about the physics of Planckbrane (another brane) in Randall–Sundrum model?

Randall–Sundrum model imagines that our universe is a five-dimensional anti-de Sitter space and the elementary particles except for the graviton are localized on a (3 + 1)-dimensional brane or branes. ...
3
votes
0answers
34 views

Cardy counting for time dependent theories

In certain limits of 2 dimensional CFT's, it is possible to compute the entropy of the theory in terms of the density of states which is given by the Cardy formula $$S = 2\pi \left(\sqrt{\frac{c_R ...
1
vote
0answers
27 views

Conformal field theories that are not conformally invariant

Is it possible to construct a field theory that is Weyl-invariant but not conformally invariant? Any references?
2
votes
0answers
55 views

Question about the superconformal index

According to arXiv:1507.08553v1, the superconformal index, defined by $$I(\beta_j) = \mbox{Tr}_{\mathcal{H}}(-1)^F e^{-\gamma\{Q,Q^\dagger\}}e^{-\sum_{j}\beta_j t_j}$$ is independent of the ...
0
votes
1answer
41 views

Fields in the action of the Non-linear Sigma Model (WZW)

I am trying to understand the action of the nonlinear sigma model in the context of understanding WZW-models. On Wikipedia, its action is given as ...
1
vote
1answer
48 views

Normal Ordering in String Theory: Polchinsky vs. all others

Polchinsky defines normal ordering in string theory as: $$:X^\mu(z,\bar z)X^\nu(w,\bar w): = X^\mu(z,\bar z) X^\nu(w, \bar w) + \frac{\alpha'}{2} \eta^{\mu\nu} \log |z-w|^2$$ and for more ...
3
votes
1answer
42 views

What is a “dynamically generated scale” physically?

A theory like QCD with massless quarks in four dimensions has no explicit mass parameters in its classical Lagrangian. At the quantum level however, instead a mass scale Λ is generated dynamically at ...
2
votes
0answers
18 views

What is the global Virasoro symmetry generators in BTZ spacetime?

This is the case of AdS3, how about BTZ? The picture is from arxiv:1506.01353.
1
vote
0answers
24 views

Generally speaking, given two CFTs, how can we check that they are equivalent?

We can calculate their central charges. And beyond this, are there some other general approaches? Or we must find an isomorphism of operators between the two theories?
0
votes
0answers
24 views

Reference request: 2D conformal field theory and functions on the triangular lattice

I don't have much of a physics background and was wondering if anyone knows what is meant by "conformally invariant" functions defined on the plaquettes of the honeycomb lattice (ie functions defined ...
3
votes
1answer
49 views

Existence of lagrangians at strong coupling

It is well known that some QFT do not admit a lagrangian formulation (like the $(2,0)$ SCFT in $d=6$). Up to my understanding, all the examples that I know of non lagrangian theories are always ...
2
votes
1answer
243 views

Can a scalar field transform nontrivially under a local special conformal transformation?

Is there any way to have a scalar field that transforms non-trivially under local special conformal transformations? Just by the index structure, I can see that the possibilities are $$\begin{align} ...
0
votes
1answer
50 views

CFT and temperature

I have tried to think about this for some time but could not really go anywhere. Sorry for the sloppy question and thanks for any pointer. My question is about CFT at finite temperature and ...
1
vote
1answer
64 views

“Irreversibility” of the RG flow

In his remarkable work, Zamolodchikov proved a theorem regarding two dimensional QFT Renormalization Group (RG) flow, describing a monotonically decreasing function in the flow parameter which is ...
0
votes
0answers
25 views

Operator product expansion in 2D cft

My question is about an orbifold CFT theory in 2 dimension. Forgetting about the details, the problem is If I want to find the OPE of two operators, let's say, $O^{++}(z)$ and $O^{--}(z)$, i can ...
3
votes
0answers
53 views

Can the terms in the microscopic model with nonzero conformal spin generate some new term(s) under RG (renormalization group) flow?

As in the book Bosonization and Strongly Correlated Systems at page 66, it says that "We see that the original perturbation with nonzero conformal spin generates the perturbation with zero conformal ...
5
votes
1answer
81 views

Orbifold actions and twist operators

A twist operator $\sigma$ is the operator that acts on the untwisted vacuum $|0\rangle$ to create a twisted vacuum $\sigma|0\rangle$. States belonging to the twisted sector of an orbifold are built on ...
3
votes
1answer
64 views

Simple conceptual question conformal field theory

I come up with this conclusion after reading some books and review articles on conformal field theory (CFT). CFT is a subset of FT such that the action is invariant under conformal transformation ...
1
vote
2answers
58 views

Central charge in energy-momentum tensor OPE

I think that general point of view about central charge in books is considering OPE $T(z) T(w)$ for different field theories and finding that general expression for the most singular term is about to ...
1
vote
1answer
64 views

Operator Product Expansion

I wonder why in OPE in CFT terms like $$ \frac{:O(z) O(w):}{(z-w)^2} $$ occur, for example in the OPE of Energy-momentum tensor with itself: $$T(z) T(w) = \frac{c/2}{(z-w)^4} + \frac{T(z)}{(z-w)^2} ...
1
vote
1answer
49 views

Globally defined solutions in bc CFT system

Consider $bc$-system which is 2-dimensional CFT of fermions: $S = \int_\Sigma d^2 z \ b \bar{\partial} c + h.c. $ where $\Sigma$ - 2-dimensional manifold of genus $p$, fields $b, c$ have ...
3
votes
1answer
80 views

Is $\phi^4$ theory in 4d conformally invariant at the classial level?

I used to believe the three following statements to be true (at the classical level only): From scale invariance full conformal invariance follows. Scale invariance is present if there are no ...
1
vote
0answers
117 views

1/m Laughlin state and $U(1)_M$ chiral CFT

I am a little confused that people claim that the edge theory of a 1/m Laughlin state corresponds to a $U(1)_m$ chiral CFT. This indicates there should be $m$ primary field operators in $U(1)_m$ ...
1
vote
0answers
113 views

Cones with deficit angle 2$\pi$ and euler characteristics

I've managed to confuse myself with cones and deficit angles. Let's consider a conical defect in 2 dimensions. So the metric is the usual one in polar coordinates, $$ ds^2 = dr^2 + r^2 d\phi^2,$$ ...
1
vote
0answers
59 views

Why is it that the conformal anomaly has to be scale invariant?

When reading about conformal anomalies, such as in this paper it is often stated that the anomaly (ie. $ \delta W[g]/ \delta \sigma$ where $ W[g]$ is the quantum effective action for gravity) must be ...
0
votes
1answer
56 views

Typo in CFT primary field transformation?

Is this a typo? Shouldn't the first formula be $$ \phi'(z', \bar{z}') = \lambda^h \bar{\lambda}^\bar{h} \phi(z, \bar{z}) $$ ? For example, with $$ \lambda = 2 $$ the pair of points $(1,1)$ gets ...
3
votes
1answer
61 views

Different OPE channels in bootstrap

Can someone quickly explain what exactly are those different channels (namely s,t,u) in OPE expansions frequently used in conformal bootstrap. Explanation with a simple example will be really helpful. ...
3
votes
0answers
62 views

How should the path integral change under a dilation?

Let's say I have a two-point function of a scalar field in flat space: $$ \langle \phi(x)\phi(y)\rangle = \int \mathcal D \phi \, \phi(x)\phi(y)\,e^{iS[\phi]} $$ Then I dilate things: $$ \langle ...
0
votes
1answer
19 views

State operator map, and scalar fields in $R\times S^{D-1}$ to $R^D$

This question is generalized version of my previous questions State operator map in $R \times S^{D-1}$ to $R^D$ , State-operator map, and scalar fields and State operator correponding $i.e$ $S^1\times ...
0
votes
1answer
33 views

State operator map in $R \times S^{D-1}$ to $R^D$

This question is relevant in my former question State-operator map, and scalar fields and State operator corrponding $i.e$ $S\times S$ to $R^2$. (which was wrong, corrected one was states in $R \times ...
1
vote
1answer
30 views

State-operator map, and scalar fields

Up so far, i have been studied state-operator correspondence, $i.e$, i have been questioned State operator corrponding $i.e$ $S\times S$ to $R^2$ which was wrong question. By studing Ginsparg's ...
1
vote
0answers
17 views

OPE of two quasi-primaries involves only other quasi-primaries and their derivatives

From Blumenhagen and Plauschinn Introduction to Conformal Field Theory, 2009: "The proof that the OPE of two quasi-primary fields involves indeed just other quasi-primary fields and their ...
1
vote
0answers
17 views

Target space Lorentz symmetry of superstrings in noncritical dimensions

Is the target space Lorentz symmetry of noncritical strings ($D \neq 26$) or superstrings ($D \neq 10$) broken or is it not? Naive arguments suggest that the mentioned anomaly does not exist, since ...
2
votes
2answers
64 views

Orbifold with discrete torsion

I'm trying to understand some of the early works of Vafa and Witten [1-3]. The way I look at orbifolds is they are the quotient space $M/G$. This is simply a quotient manifold when the action of $G$ ...
1
vote
0answers
38 views

CFTs in the phase space of QFTs [closed]

In the cases I have encountered a CFT is often realised as a RG fixed POINT of the RG flow. Is it also possible to have a whole family/mine/manifold of CFTs instead?
2
votes
1answer
51 views

Definition of primary fields actually leads to a Witt algebra with a minus sign?

Let's take as an example Di Francesco et al. but every source I am aware of is doing the same. First of all, the Virasoro algebra is usually defined as $$[L_m,L_n] = (m - n)L_{m+n} + \frac{c}{12} m ...
1
vote
0answers
54 views

Linear Dilaton CFT

I´m doing the exercises on the Tong lectures of String Theory, in particular Problem Sheet 2: Consider the tensor: $T(z) = \frac{-1}{\alpha '} :\partial X(z) \partial X(z): - Q \partial^2 X$. By ...
0
votes
0answers
40 views

DBI action with Weyl Invariance

The DBI action, given by $S_{Dp}=-T_p\int d^{p+1}\xi e^{-\phi(\xi)}\sqrt{-\textrm{det}\left(G_{ab}(\xi)+B_{ab}(\xi)+2\pi{\alpha}'F_{ab}(\xi)\right)}$ is diff and Poincaré invariant. I want to ...
2
votes
0answers
32 views

In what situation will a conformal transformation leave the vacuum invariant

Recently I am reading Francesco's CFT. In section 5.4.2, it considers a generic CFT living on the entire complex plane and maps this theory on a cylinder of circumference L by the transformation: $$ ...
1
vote
1answer
64 views

Error in Kac's “Vertex algebra for beginners” proof that a Wightman QFT gives rise to a vertex algebra?

Given $$ i[Q_k,\Phi_a(x)]=((x_0^2-x_1^2)\partial_{x_k}-2\eta_k x_k E - 2\Delta_a \eta_k x_k) \Phi_a(x), \quad (1.1.8) $$ applying a coordinate change $t= x_0-x_1$, $\bar{t}= x_0+x_1$ and defining $$ ...
0
votes
1answer
52 views

OPE of parity even theories in CFT.

If I consider an OPE of some operators, which belong to a theory where parity is not violated, will I have a constraint on the kind of operators appearing in the right hand side ? For example, I ...
1
vote
1answer
114 views

Conformal properties of the energy-momentum tensor and Schwarzian derivative

Polchinski Vol. 1 (Sec. 2.4): I'm trying to understand the Eq. 2.4.26 where he shows how the stress tensor transforms under a conformal transformation ($z \rightarrow w$): $$(\partial w)^2 T(w) = ...
2
votes
1answer
132 views

Operator-state correspondence in CFT: computing operator for given state

In 2D CFT there is a bijection between states and operators. In one direction it is easy: if $\phi(z)$ is a primary field then $|\phi \rangle:=\lim_{z \to 0} \phi(z)|0\rangle$ is a highest weight ...
5
votes
0answers
54 views

Dual of the Identity operator (AdS/CFT)

We know that in a CFT the spectrum of gauge invariant operators must contain an Identity operator (for the operator algebra to close). For those CFTs that admit a holographic dual what does the ...
0
votes
1answer
95 views

Relationship between modular transformations and anyon braiding

In the context of anyon braiding, we have $S$ and $T$ matrices which describe the mutual and self statistics of anyons. In the context of conformal field theory on a torus, we have modular ...