It's about this "" long.
At present, it can't be proven empirically because they have no way of devising any tests which can physically measure objects that small or dimensions of spacetime other than what we can see. It's a mathematical construct which is, at present, our best theory for explaining why things are the way they are.
Think of cosmic strings as being akin to a simple harmonic oscillator...like the strings of a guitar. The mathematics are actually very similar except that strings are dealing with packets of energy that define spacetime and all that's in it, whilst the guitar strings are dealing with sound. You have a fundamental tone and an infinite number of overtones, all with an unique vibration. Each vibration, or overtone, defines a particular characteristic of an atom, or subatomic particle. It also defines the field of the particle and how it behaves. How it interacts (or doesn't interact) with everything else. Those overtones can change depending on whether they lose or gain energy or interact with other overtones/strings.
You could say that reality is fundamentally musical...and so is mathematics