an antenna is basically a capacitor. theremins operate by responding to changes in the antenna's capacitance, which occur when objects (like your hand) move closer to, or further away from it.
if you want to use arduino to make an antenna-based controller or theremin, you need to figure out a way in which it can 'read' the capacitance of the antenna. converting the antenna capacitance to a variable resistance value (in other words, turning it into a potentiometer) may require some complex, or at least unnecessary, circuitry. i've been experimenting with quantum's QT300 capacitance-to-digital sensor, which dierctly measures the capacitance of an object connected to it, then returns a 16-bit digital value relating to the measurement. there may be other ways to measure capacitance - perhaps you could try using arduino to directly measure the antenna capacitance somehow?
let me know if you have any luck!
jon