# Questions tagged [conformal-field-theory]

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 theory, statistical mechanics, and condensed matter physics.

939 questions
Filter by
Sorted by
Tagged with
24 views

### Picture Number Operator in String Theory

My question concerns the ghost picture charge/picture number operator in the RNS formalism of Superstring theory. In particular I refer to page 403 of "Basic Concepts of String Theory" by R. ...
64 views

### What is my mistake in solving the commuation relation $[P_\mu , K_\nu]$

The aim is to obtain the commutation relation: $$[P_\mu , K_\nu]= -2\eta_{\mu\nu}D + 2L_{\mu\nu}$$ I have been trying to solve this for a while now and I get different answers, but not the one I am ...
39 views

### Checking $\xi$ solves the conformal killing equation

Problem: I am trying to prove that, using: $$\xi^\mu (x) = a^\mu + \omega ^\mu_\nu x^\nu + \sigma x^\mu + b^\mu x^2 -2b_\nu x^\nu x^\mu \tag{1}$$ and $$\kappa = \sigma -2b_\nu x^\nu \tag{2}$$ ...
51 views

### Argyres-Douglas CFT

Adding of mass in supersymmetric gauge theories will affect structure of moduli space by creating new singular point (picture and some statements from Matteo Bertolini: Lectures on Supersymmetry): ...
41 views

61 views

46 views

In class it was shown that $$i[Q_\epsilon,T^{\mu\nu}] = -(\epsilon\cdot\partial)T^{\mu\nu} - \partial_\rho (\epsilon^\mu T^{\rho\nu}) + \partial^\nu(\epsilon_\rho T^{\rho\mu})$$ with $$Q_\... 2answers 51 views ### Where is this Virasoro null from? Let's consider the Virasoro algebra with a generic c. Take a primary |h\rangle and I try to look for its level-9 nulls: Mathematica spits out 3 solutions$$ h = \frac{1-c}{3}, \quad \frac{1}{3}(53-...
81 views

If one will consider free fermion on torus,one will face with different spin structures. There are four spin structures, usually labeled ±±. The ++ spin structure has a single positive chirality zero-...
55 views

### Conformal Invariance of the Scalar Field

Consider a scalar field with action $$S(\phi)=\int_Md^Dx\partial_\mu\phi\partial^\mu\phi.$$ Following the book on Conformal Field Theory of Di Francesco, Mathieu and Sénéchanl, they claim that under a ...
39 views

### Kac-Moody primary OPE

I am reading a paper and on page 13-14 (PDF page 15-16), they say that, The fermionic generators [$G^\pm$ and $\tilde{G}^\pm$] are Virasoro and affine Kac-Moody primaries with weights $h= 3/2$ ...
136 views

60 views

### Constraining the 2-point correlation function

Consider the two-point function $$\langle\mathcal{O}_1(x_1)\mathcal{O}_2(x_2)\rangle=f(x_1,x_2)$$ If the operators are in a CFT, we can constrain this function using the symmetries of the theory. ...
69 views

148 views

A Question in Classical Field Theory $\underline{\text{Assumption 1}}$: The definition of a transformation specifies how both the coordinates and the fields transform: They are namely $(1$-$1)$ and $(... 0answers 62 views ### Witten's description of WZW conformal blocks I am reading this paper by Witten - Geometric Langlands From Six Dimensions. In section 4.1, he gives a description of the vector space of conformal blocks of the current algebra associated to a ... 1answer 60 views ### Minimal models and Lattice models How does one see that the minimal model M(4,3) is the Ising model ? And how can I argue out that the fields contained in M(6,5) but with the non-diagonal modular invariant partition function ... 1answer 103 views ### OPE of stress tensor in CFT I come aross an OPE between stress tensor components in CFT which is \begin{equation} T(z)\bar{T}(\bar{w})\sim -\frac{\pi c}{12}\partial_{z}\partial_{\bar{w}}\delta^{(2)}(z-w)+... \end{equation} I am ... 1answer 71 views ### What are the necessary conditions for a CFT to have a holographic dual? [duplicate] The number of degrees of freedom of a CFT is given by its central charge$c$. From the bootstrap point of view, any CFT is characterized by the knowledge of its "CFT data", i.e. the scaling dimensions ... 0answers 55 views ###$T$-duality symmetry of$SU(2)_1\$ WZW model

For bosons at self-dual radius, the CFT has T-duality symmetry. My question is can we realize this symmetry on the lattice model? for example antiferromagnetic spin chain.