In physics the word theory is used synonymously with mathematical model or mathematical framework. The theory is a mathematical construction that can be used to describe physical phenomena. A theory should, at least in principle be falsifiable, that is make predictions that can be tested.
People who are not trained in physics take theory to mean either “hypothetical” or loosely an “idea”. One may hear “but it is only a theory”, which takes the physics use of the word theory out of context.
A theory, in the sense of modern physics must by definition be phrased in mathematics. We need something to mathematically manipulate and calculate things that can be tested against observation. Without the mathematical framework it is hard to judge if an “idea” has any merit or not.
Often by theory physicists may have something a little more specific in mind, they often mean a specified action or Lagrangian. Most of physics can be stated in terms of actions and so it usually makes sense to start there. Again the action or equivalently the Lagrangian are mathematical notions.