I have been trying to do all the calculations in the Green, Schwarz and Witten Superstring Theory textbook.

At the end of chapter 3, the author did one-loop calculation for Weyl invariance for the bosonic string, in section 3.4.2 and 3.4.5. In the latter section more fields were included, and not much calculation detail was given.

The actions are

$S_1=\frac{-1}{4\pi\alpha'}\int d^2\sigma\sqrt h h^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu g_{\mu \nu}$

$S_2=\frac{-1}{4\pi\alpha'}\int d^2\sigma \epsilon^{\alpha \beta}\partial_\alpha X^\mu \partial_\beta X^\nu B_{\mu \nu}$

$S_3=\frac{1}{4\pi}\int d^2\sigma \sqrt h \Phi (X^\rho) R^{(2)}$

I consider those one-loop calculations to be very good exercise, but as a beginner in string theory I find myself not able to do them.

Therefore may I ask if there are some notes/papers in literature that give explicit calculation or point out key steps? Thank you very much!

This post imported from StackExchange Physics at 2014-04-14 16:23 (UCT), posted by SE-user Han Yan