I want to understand the argument being made from equation 6.1 to 6.5 in this paper between pages 27-28

6.2, 6.4 and 6.5 are completely out-of-the-blue to me and I have no clue as to from where they come.

My impression is that this part of the argument in the paper is self-contained and it would be great if someone can help me get these equations.

If people want it then I can try to paraphrase here again as to what is written in the paper but I have actually nothing to add to what is already written in that paper..


Equation 6.2 is just the Liovelle Action, the action principle for the Liouville Field, which is well-known from the familiar conformal gauge.

$$S_L=\frac{c}{96\pi}\int_\mathcal{M}\left(\dot\varphi^2-\frac{16\varphi}{\left(1-\lvert t\rvert^2\right)^2}\right)\mathrm{d}^2t$$

... along with some trivial facts about partition functions.

You could of course think of it as the $Z_\mathcal{M}$'s (partition functions) of the metrics being related by the $S_L$'s in the same way that the metrics are related by the Liouvelle field.

And yes, I don't know how to spell "Lioivulle" properly.

  • 2
    $\begingroup$ You had it right the second time: "Liouville" $\endgroup$ – Ketil Tveiten Dec 10 '13 at 8:33

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.