# String Theory, Ghost SCFTs

In the section on free SCFTs in chapter 10, in equation (10.1.19) of Polchinski's volume 2, it isn't clear to me how he writes down the fermionic stress tensor. Shouldn't that correspond to a world sheet supersymmetry transformation? If so, how is he able to write that expression without mentioning what the corresponding supersymmetry transformations are?

Thanks.

• I am sure that you would have a better chance of an answer if you could include the equation and surrounding text in your post. Even a photo. – user108787 Nov 11 '16 at 4:20
• I think the pedagogy here is that $T_F$ is chosen to satisfy the general N=1 superconformal algebra in OPE form, given by (10.1.15a-c). From the OPEs of $T_F$ with the fields $b,c, \beta$ and $\gamma$, the superconformal transformations can be found. They can also be found in the literature. – Meer Ashwinkumar Jan 13 '17 at 13:41

## 1 Answer

I think the pedagogy here is that $T_F$ is chosen to satisfy the general $N$=1 superconformal algebra in OPE form, given by (10.1.15a-c). From the OPEs of $T_F$ with the fields $b,c, \beta$ and $\gamma$, the superconformal transformations can be found. The explicit forms of these transformations should be available in the literature.