Tagged Questions
8
votes
1answer
194 views
Is there a “covariant derivative” for conformal transformation?
A primary field is defined by its behavior under a conformal transformation $x\rightarrow x'(x)$:
$$\phi(x)\rightarrow\phi'(x')=\left|\frac{\partial x'}{\partial x}\right|^{-h}\phi(x)$$
It's fairly ...
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 ...
5
votes
2answers
196 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 ...
8
votes
1answer
102 views
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 ...
6
votes
1answer
55 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 ...
7
votes
3answers
100 views
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 ...
6
votes
3answers
161 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 ...
8
votes
1answer
93 views
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 ...
7
votes
2answers
51 views
“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 ...
9
votes
1answer
72 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
89 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 ...
12
votes
2answers
59 views
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 ...
10
votes
2answers
44 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 ...
13
votes
2answers
128 views
Which CFTs have AdS/CFT duals?
The AdS/CFT correspondence states that string theory in an asymptotically anti-De Sitter spacetime can be exactly described as a CFT on the boundary of this spacetime.
Is the converse true? Does any ...
8
votes
1answer
258 views
AGT conjecture and WZW model
In 2009 Alday, Gaiotto and Tachikawa conjectured an expression for the Liouville theory conformal blocks and correlation functions on a Riemann surface of genus g and n punctures as the Nekrasov ...
7
votes
1answer
78 views
Characters of $\widehat{\mathfrak{su}}(2)_k$ and WZW coset construction
I am currently studying affine Lie algebras and the WZW coset construction. I have a minor technical problem in calculating the (specialized) character of $\widehat{\mathfrak{su}}(2)_k$ for an affine ...
14
votes
1answer
54 views
Miura transform for W-algebras of exceptional type
Miura transform for W-algebras of classical types can be found in e.g. Sec. 6.3.3 of Bouwknegt-Schoutens. Is there a similar explicit Miura transform for W-algebras of exceptional types, say, E6? It's ...
5
votes
1answer
62 views
Choice and identification of vacuums in AdS/CFT
I know how we define a vacuum in flat space QFT and also in a curved space QFT. But, can somebody tell me how do the choice of vacuum state in (say) the CFT side of AdS/CFT changes the choice of ...
13
votes
2answers
64 views
Uniqueness of supersymmetric heterotic string theory
Usually we say there are two types of heterotic strings, namely $E_8\times E_8$ and $Spin(32)/\mathbb{Z}_2$. (Let's forget about non-supersymmetric heterotic strings for now.)
The standard argument ...
20
votes
5answers
77 views
Connections and applications of SLE in physics
In probability theory, the Schramm–Loewner evolution, also known as stochastic Loewner evolution or SLE, is a conformally invariant stochastic process. It is a family of random planar curves that are ...
14
votes
1answer
109 views
Do Gauge Theories (CFTs) Have Phase Transitions as the 't Hooft Coupling is Varied?
With an eye toward AdS/CFT, I'm wondering if large $N$ CFTs have a (quantum) phase transition as the 't Hooft coupling is varied. To be more specific -- if I look at correlation functions of ...
19
votes
1answer
33 views
What is known about the classification of N=4 SCFTs with central charge 6?
I was talking about K3 surfaces with some physicists, and one of them told me that the N=4 superconformal field theories with central charge 6 are expected to be relatively scarce. In particular, one ...
12
votes
4answers
2k views
A pedestrian explanation of conformal blocks
I would be very happy if someone could take a stab at conveying what conformal blocks are and how they are used in conformal field theory (CFT). I'm finally getting the glimmerings of understanding ...
