What is arithmetic circuits indeed?
The whole point is that in the Aritmetic Circuit (AC) model we take a field and use field operations (+,*) as building blocks.
Each field operation is represented as a single output multiple input gate.
The total number of gates and the depth of the AC are typical measures of complexity. Size and bit structure of inputs does not explicitly come into it, each operation is considered of some fixed complexity.
The goal is to find the minimum complexity circuit realizing a certain formula.