The SOC constraints

how to use cvx code to describe the SOC constraint like (58)

What are f_3(z), f_4(z)? Why is a norm involving the square root of something (f_3(z) ) convex?

Please don’t keep throwing up images from who knows where with no explanation.of what anything is.

Constraint (57) looks like just f_3(z)\leq f_4(z). Can we have more info or a link to the paper?