There is a lot of things in string theory that are very tightly coupled to the special-ness of 2d CFTs. These features are not continuous in the size of the second dimension, i.e. they don't disappear when you make the second dimension smaller.
@Slereah Also: There are only 5 string theories, but a plethora of quantum field theories. There already is a well-accepted way to go from ST to QFT: Compute the stringy amplitudes, observe they are the amplitudes of a 10d SUGRA amplitude.
You know, that may well be. Most of string theory isn't really concerned with this basic part of string theory, even if it is a large part of most books on the subject
You can even do a non-relativistic limit to show the action reduces to the classical action for a string to see why the tension $T$ is a string tension, it's in BBS
What you need to see is that, in contrast to QFT, the computation of the stringy amplitude in free space is only the beginning of string theory, since that only gets you a theory in 10d Minkowski space that's completely disconnected from anything physical
But in the end, the only possible limits you could get are, once again, the 5 10d SUGRAs. I wouldn't be surprised if you could work this limit out in detail, but you'd just get the result everyone already knew
Another part where you probably have to wave your hands really hard is to argue how the sum over worldsheet topologies turns into a sum over graph topologies in any sort of limit
I guess the first step would be showing that the propagator of a single string contracts to the propagator of a relativistic particle
@bolbteppa I'd feel better about those kinds of demonstrations if we defined the NG action as $$S = \frac{m}{\int d\sigma} \int \sqrt{\gamma} d\sigma d\tau$$
The relativistic action is just the arc length up to a constant you determine from the non-relativistic limit, similarly the NG action is just the area up to a constant you also determine from the non-relativistic limit (Becker Becker Schwarz Ex. 2.7)
Of course such an area is going to have to come from integrating the worldlines making up the world-sheet and reduce to the action of a point particle in some limit
But the time evolution of these states is completely and solely defined by the stringy sum over worldsheets. You can't really ask about how one of them propagates to another.
Please write down what expression you actually think is "the propagator of a single string"
@Slereah So, if you properly do the gauge fixing for $\gamma$ there, I'm pretty sure this is just the partition function for the 2d CFT that lives on the world sheet
@Slereah No, the point is that you need to fix the gauge freedom one has in choosing the metric, as one also does in the full string amplitude (buzzword: moduli of Riemann surfaces)
Setting $X^0 = \tau, X^1 = \sigma$ and leaving the $X^i$ as fields we have \begin{align} S &= - T \int d \tau d \sigma \sqrt{- \det \gamma_{\alpha \beta}} = - T \int d \tau d \sigma \sqrt{- \det \partial_{\alpha} X \cdot \partial_{\beta} X } \\ &= - T \int d \tau d \sigma \sqrt{- \det \begin{bmatrix} \partial_{\tau} X \cdot \partial_{\tau} X & \partial_{\tau} X \cdot \partial_{\sigma} X \\ \partial_{\sigma} X \cdot \partial_{\tau} X & \partial_{\sigma} X \cdot \partial_{\sigma} X \end{bmatrix} } \\
@EmilioPisanty I have maybe a weird take on this. I don't fault a user who is discomfited by something and flags rather than speaking up. But I don't like rooms where the custom is to chuck flags around and nary a word is said (until "stop flagging me, bitch!" starts up).
Apologies if this is a silly question, but why does a reference frame exist in which the average velocity of CMB photons is zero? Why don’t they follow a distribution without a mean, like the Cauchy distribution? Is there a deep reason for this?
