I'm attempting to try and learn basic ideas in conformal field theory without reading a big yellow book, or other big books. (Edits to this question are highly sought and welcome)
My question is the following:
How does one construct the torus partition function of the Ising model conformal field theory in particular or just for a simple free scalar field theory that is conformally invariant, and also find the corresponding minimal model?
Below is my convoluted idea/attempt of how to attempt this.
0)I have managed to convince myself that I did the Hubbard-Stratonovich transformation taking me from the Ising model to the "euclidean $\phi^4$" theory. I don't know if this theory is conformally invariant. I can probably check. Technically, if it has a mass-like term it isn't. If it is not I want an excuse to kick out the problematic terms and call it free or something.
I then want to do a few weird things for the purpose of learning.
i) I feel like computing the two-point correlation function which I am thinking to be just the green function of this theory and then equating it to $\frac{1}{(|x_2 - x_1|)^{2 \Delta}}$. My goal is to extract $\Delta$ this way.
ii) I want to calculate the Casimir energy of $\phi^4$, on a cylinder. This is supposed to be something like $E = - \frac{2 \pi(c + \bar{c})}{24}$
iii) I want to also compute c
iv) I want to use c to construct a partition function. I was going to do something silly but I have noticed that people define $H$ on a cylinder and then a partition function on a torus. I have no idea why excluding some stringy reasons. At any rate, $H$ seems to usually be defined as $L_0 + \bar{L} - \frac{c + \bar{c}}{24}$, and then $Z[\tau] =Tr e^{2 \pi (Im \tau) H}$
iv) At this point I will have c, and we can check that (p,q) =(4,3) minimal model is gotten hopefully? As this seems to be what the Kac table (which I am still trying to figure out) seems to say is the critical limit of the Ising model.