# Spin of the sress-energy tensor in d=2

1. Mar 1, 2008

### navocane

If we suggest a generic quantum field theory and assume that the theory is Poincare-Invariant (i.e. the corresponding Ward-Identities are satisfied) than the stress energy tensor in two dimensions can be written in terms of complex coordinates $$z,\bar{z}$$as
$$T^{zz}(z,\bar{z})=T^{00}-T^{11}-2iT^{10}$$
$$T^{\bar{z}\bar{z}}(z,\bar{z})=T^{00}-T^{11}+2iT^{10}$$
$$T^{z\bar{z}}(z,\bar{z})=T^{\bar{z}z}(z,\bar{z})=T^{00}+T^{11}\equiv -\Theta(z,\bar{z})$$
My question is how to find the Spin of the components $$T^{zz},T^{\bar{z}\bar{z}},\Theta$$. The authors of the paper I'm studying claim
$$ST^{zz}=2, ST^{\bar{z}\bar{z}}=-2 , S\Theta=0$$ but i don't see how . Can anyone help?