The h Bar

2:02 PM

@ACuriousMind do you have a reference for asymptotic series and all this stuff

@0celo7 The string perturbation series is also an expansion around the "classical free background" of string theory, which is essentially given by the precise choice of CFT that lives on the world sheets.

0celo7

do your QFT notes talk about it

ACuriousMind

@0celo7 No. I only know what you can find by googling.

(or not, given your Google skills :P)

0celo7

@ACuriousMind so?

ACuriousMind

For the "string background", see also landscape of string vacua

0celo7

2:03 PM

So is the "classical free background" of string theory not the "metric on the bulk" or whatever

ACuriousMind

@0celo7 It's the "choice of target space" together with "choice of CFT"

0celo7

what does "choice of CFT" mean

ACuriousMind

Where "target space" means choosing the compactification of the 10D space, I think

0celo7

you're not explaining very well :/

ACuriousMind

@0celo7 lol, that's because I don't understand it very well

There's a reason my top tags are quantum-mechanics and quantum-field-theory, not string-theory :P

0celo7

2:06 PM

well I don't think BBS will explain it either

what does "choice of CFT" mean??

ACuriousMind

Choosing the central charge and the conformal weights that are allowed to appear, at least in the range of minimal models :P

But since ST fixes the charge to 0 and the weights to 1 for the physical states, I'm not sure that's what is meant here

0celo7

why :P

see, you think I don't know what that means

well screw you

I know some of those words

ACuriousMind

@0celo7 Because it is true, but not very helpful

0celo7

damn, what are the conformal weights

sounds familiar

$h$ and $\bar h$

thank you BLT

ACuriousMind

@0celo7 Eigenvalues of $L_0$ and $L_0^\dagger$

0celo7

2:10 PM

@ACuriousMind which are $h$ and $\bar h$

ACuriousMind

Or, yes, $h$ and $\bar h$ (hate that notation, btw, because $\bar h$ is not the conjugate of $h$)

0celo7

so what does it mean "allowed to appear"

ACuriousMind

@0celo7 Well, one can define a CFT purely by the central charge and the conformal weights, since these fix the structure of the space of states (the space of states has to be a unitary representation of the Virasoro algebra, and generic ladder operator methods show those representations can be labeled by $c$ and the allowed conformal weights (and only certain weights are possible for certain charges to begin with)). But I'm not sure that's what the string people mean by choice of CFT

(Since charge and weights are fixed by ST AFAIK)

I'm also unsure how the fermions appear in this way.

0celo7

@ACuriousMind hey I knew that first sentence

lol you've just read the nLab stuff

you don't really understand this :P

ACuriousMind

The CFT stuff I don't have from nLab. The string stuff...well, yes :D

@0celo7 I said that already

0celo7

2:21 PM

@ACuriousMind now it's confirmed

Slereah

@ACuriousMind T is not the conjugate of I either

0celo7

I don't think BBS talks about this either...it might later on

I'm like half way through chapter 6 I think

@Slereah hah

ACuriousMind

@Slereah ::slow clap::

Qmechanic

@Slereah : Reminds me of the saying There is no I in TEAM.

0celo7

@ACuriousMind I never understood this part in BLT.

ACuriousMind

2:28 PM

@0celo7 ...and what exactly do you not understand?

0celo7

@ACuriousMind how to get (9.3)

and (9.4)

@JohnDuffield If I ask a question about non-mainstream physics, it will get shut down.

As for the other stuff...I's not sure what you're saying. By what mechanism does light go "round and round"?

I don't think "round and round" is a null geodesic, is it?

ACuriousMind

@0celo7 Hm

@0celo7 Are $h,g$ phases, or arbitrary complex numbers?

(I hope they're phases, then I think I at least have the idea of whats happening)

0celo7

@ACuriousMind Yes, that's what the footnote says.

ACuriousMind

2:46 PM

@0celo7 Okay, then $h$ and $g$ tell you how often you have to go around the torus until the boundary values are equal. The modular transformation just changes the size of the torus, but not its modular structure. So on a torus with a different size, the same field has to go around the torus a different number of times to be equal because the torus is larger/smaller.

0celo7

Alright, but how do I derive (9.3)?

I get the concept.

ACuriousMind

That is, if we phrase the tori as lattices in the complex plane (spanned by $\lambda_1,\lambda_2$), then the function $\psi$ is always periodic with the period length $n_i\lambda_i$, where $n_i$ is given by solving $h^{n_i} = 1$.

0celo7

Ok.

ACuriousMind

Now, you have to express the period lengths by $\lambda'_i$.

0celo7

I see.

I'll figure that out...later.

ACuriousMind

2:52 PM

And that gives you some $h'$ and $g'$ after some manipulation, which will be the powers of $h$ and $g$ they write there.

ACuriousMind

3:25 PM