9
votes
1answer
140 views

Why do we assume local conformal transformations are symmetries in 2D CFT

The global conformal group in 2D is $SL(2,\mathbb{C})$. It consists of the fractional linear transforms that map the Riemann sphere into itself bijectively and is finite dimensional. However, when ...
6
votes
1answer
286 views

Is Conformal Symmetry Local or Global?

I'm just brushing up on a bit of CFT, and I'm trying to understand whether conformal symmetry is local or global in the physics sense. Obviously when the metric is viewed as dynamical then the ...
3
votes
0answers
195 views

Traceless of stress-energy tensor in $d=2$

This is a question regarding Francesco, section 4.3.3. In this section, he considers the two-point function $$ S_{\mu\nu\rho\sigma}(x) = \left< T_{\mu\nu}(x) T_{\rho\sigma}(0)\right> $$ He then ...
3
votes
1answer
210 views

What are the conserved charges related to the Virasoro generators?

I have just learned from reconsidering my demystified book, that when conformally maping the worldsheet of a closed string to the complex plain by using the transformation $z = e^{\tau + i\sigma}$ ...
9
votes
4answers
333 views

Symmetries of a Free Massless Scalar in Two Dimensions

On p. 49 of Polchinski's book, he says: "Incidentally, the free massless scalar in two dimensions has a remarkably large amount of symmetry -- much more than we will have occasion to mention." Does ...
3
votes
1answer
169 views

Question on Section 9.1.3 in “Conformal Field Theory” by Philippe Di Francesco et. al

Question on Section 9.1.3 in "Conformal Field Theory" by Philippe Di Francesco et. al. The basic idea of the Coulomb-gas formalism is to place a background charge in the system, making the $U(1)$ ...
2
votes
2answers
308 views

Invariance of Maxwell's Equations under inverting variables - Reference and use

Some months ago, an ArXiv paper mentioned in passing that Maxwell's Equations were invariant under reciprocating the variables, or at least this results in a dual set of Maxwell Equations. (Actually I ...
1
vote
0answers
192 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 ...
4
votes
1answer
75 views

How can we have massive states of strings and CFT on the string worldsheet at the same time?

Ok, so we can have conformal invariance on a string world sheet. However, it is well known that to preserve conformal symmetry we require states to be massless. So how is it that string theories ...
6
votes
2answers
447 views

Why are conformal transformations so prevalent in physics?

What is it about conformal transformations that make them so widely applicable in physics? These preserve angles, in other words directions (locally), and I can understand that might be useful. Also, ...