I am reading Witten's paper on topological field theories, in specific the topological twist in page 359. In order to perform the twist he takes the diagonal subgroup of $K = SU(2)_{\text{Right}} \times SU(2)_{\text{Isospin}}$ where the first comes from the $SU(2)_{\text{Left}} \times SU(2)_{\text{Right}} \simeq SO(4) $ while the latter is part of the $\mathcal{R}$-symmetry group $SU(2)_{\text{Isospin}} \times U(1)_{\mathcal{R}}$.

What does it mean to take the diagonal of $K$ and how can I understand how the representations of the sections/fields change after the twist? I mean, he says it is "easy to see" how the fields transform under the new global group but I cannot see it.